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EXPOSITION AND ILLUSTRATION 
IN TEACHING 



THE MACMILLAN COMPANY 

NEW YORK • BOSTON • CHICAGO 
ATLANTA • SAN FRANCISCO 

MACMILLAN & CO., Limited 

LONDON . BOMBAY • CALCUTTA 
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EXPOSITION AND ILLUSTRATION 
IN TEACHING 



BY 



JOHN ADAMS, M.A., B.Sc. 

PROFESSOR OF EDUCATION IN THE UNIVERSITY 
OF LONDON 



THE MACMILLAN COMPANY 
1910 

All rights reserved 



v^ 



COPYEIGHT, 1910, 

By the MACMILLAN COMPANY. 
Set up and electrotyped. Published January, 1910. 



Noriwaotj ^reS3 

J. 8. Gushing Co. — Berwick & Smith Co. 

Norwood, Mass., U.S.A. 



g'CU^o^^Mjo 



TO MY OLD MASTER 
MR. JAMES LIDDELL 



Digitized by the Internet Archive 
in 2010 with funding from 
The Library of Congress 



http://www.archive.org/details/expositionillustOOadam 



CONTENTS 

CHAPTER TAGrS 

I. Nature and Scope of Exposition and Illustra- 
tion 1 

11. Mental Content 37 

III. Mental Activity 65 

IV. Mental Backgrounds 91 

V. Suggestion . 116 

VI. Conditions of Presentation 145 

VII. Beginnings in Exposition 167 

VIII. Order of Presentation 187 

IX. Exemplification and Analogy 228 

X. The Story as Illustration 250 

XL Elaboration 275 

XII. Degree in Illustration 297 

XIII. Material Illustrations 317 

XIV. The Picture as Illustration 336 

XV. The Diagram as Illustration 354 

XVI. Dangers of Illustration 391 

XVII. The Torpedo Shock 416 



vii 



EXPOSITION AND ILLUSTEATION 
IN TEACHING 

CHAPTER I 

Nature and Scope of Exposition and 
Illustration 

Applying the principles to be laid down in what fol- 
lows, it is well to make a beginning in some region of 
knowledge that is common to all intelligent educated 
people. A good dictionary may be fairly taken to 
represent such a region. What the dictionary tells us 
about Exposition and Illustration will probably be 
admitted to be common property, and therefore a suit- 
able starting-point for a treatment that will introduce 
points of view that may be unfamiHar to the reader. In 
teaching, it is now generally admitted that we ought 
rather to lead up to a definition than to start from one. 
In what follows, the definitions as found in the diction- 
ary will not be treated as ends in themselves, but merely 
as the common basis from which reader and writer may 
make an intelligible start. This chapter will concern 
itself not so much with the explanation of the defini- 
tions which it borrows from the dictionary as with the 
elaboration of the connotation of the terms Exposition 
and Illustration in their relation to teaching. 

In Sir James A. H. Murray's ^'New English Diction- 

B 1 



2 EXPOSITION AND ILLUSTRATION IN TEACHING 

ary on Historical Principles '* we find under the word 
expound f the following meanings : — 

1. To set forth, declare, state in detail (doctrines, ideas, principles ; 

formerly used with wider application). 

2. To explain, interpret : 

(a) gen. To explain (what is difficult or obscure) ; to state 
the signification of ; to comment on (a passage or an author) . 

(6) esp. To interpret, comment upon (Scripture, religious 
formularies, etc.) . Now chiefly with reference to homiletic 
exposition. 

We may safely neglect the more literal meanings 
attached to exposition, such as "putting out of," "ex- 
posure," "putting to public view"; just as we need not 
seriously consider the archaic use in Hudibras: "He 
expounded both his pockets," or Littre's "putting in 
the pillory." So far as the teacher is concerned, two of 
the accepted meanings stand out as of importance: "to 
set forth" and "to explain or interpret." In the ordi- 
nary practice of the schoolroom these two meanings are 
not usually distinguished from each other, because, as a 
matter of fact, the purpose of setting forth anything is 
to explain it to the pupil. If we set a matter clearly 
before another, we feel that we have explained it. If 
to a wayfarer we set forth his route, we feel that we have 
explained a matter about which he was in doubt. A 
clear statement of the Binomial Theorem is generally 
regarded as in some sort an explanation of that theorem. 
There are those who question whether the teacher can 
und^r any circumstances do more than make just such 
a presentation. Jacotot, the founder of the "Universal 
Method" of teaching, is usually true to his reiterated 
principle that "a teacher is never necessary to man," ^ 

> Enseignement Universel, p. 304. 



NATURE AND SCOPE 3 

but in a moment of unusual generosity he admits that 
''a teacher is useful to men, he is necessary to children, 
but a teacher who explains [uri maitre explicateur] is 
deadening [abrutissant\J^ ^ The negativeness of the 
teacher's work from this point of view is obvious. In 
the words of one of Jacotot's editors: '^In fact, the 
Founder limits himself to saying: ^Here is a book; 
learn Latin/ " 

But while the two meanings of Exposition — setting 
forth and explaining — to a certain extent overlap, 
they imply a real distinction that is worth the teacher's 
attention. While we are mainly interested in discover- 
ing how to present certain matters in the way best 
suited to render them intelligible to the pupil, we are 
none the less setting them forth. The first meaning of 
Exposition, in fact, implies the presentation of new 
matter, the second the explanation or interpretation of 
matter already known to, but not yet fully understood 
by, the pupil. The first meaning, ^^ setting forth," 
corresponds to what is usually understood in school 
and college by the verb demonstrate. This word, which 
literally means to show or point out, has acquired the 
added connotation of '^for a purpose.'' A demon- 
strator in a college is not a man who points out merely, 
but one who shows the meaning of what he points out. 
As the dictionary has it, he '' exhibits and explains." 
Still, the fact remains that in both the first meaning of 
expound and in the general meaning of demonstrate 
there is the notion of supplying new matter, so that this 
presentation of new matter may be regarded as an es- 
sential part of Exposition, though it need not be found 
at all stages of Exposition. We shall see when we come 

^ Avant-propos de cette Quatrieme l&dition : De la Langue maternelle. 



4 EXPOSITION AND ILLUSTRATION IN TEACHING 

to deal with Illustration that the same distinction arises 
between the introduction of new matter and the manip- 
ulation of old. 

It has to be observed that for our present purpose we 
are treating the subject of Exposition from the point of 
view of the teacher. It is possible to regard it entirely 
from the pupil's standpoint. When this is done, Ex- 
position is dealt with as a part of composition, and 
ranks as coordinate with narration and description. 
As such it enters into the ordinary school curriculum, 
and in many cases receives a considerable amount of 
attention. Naturally the principles of Exposition must 
remain the same whether practised by the pupil or by 
the teacher, but the conditions under which the princi- 
ples are applied in the two cases are so different that a 
separate treatise is required for each.^ 

It will be noted that the dictionary lays stress on the 
fact that the things to be set forth are '^doctrines, ideas, 
principles," the obvious inference being that Exposition 
has nothing to do with material things, that we can no 
more expound a steam engine than we can expound our 
pockets. But while it is bad English to speak of ex- 
pounding a locomotive, we may correctly speak of 
expounding the principles on which the locomotive 
works. This does not, after all, mean that the concrete 
is removed from the realm of Exposition, but merely 
that Exposition can deal with the concrete only in terms 
of ideas. The contributions of the senses must be 
taken for granted by the expositor. His business is so 
to arrange the mental results of sensations that they 

^ For a treatment of the subject as a part of the curriculum, see 
Exposition in Classroom Practice, by Mitchill and Carpenter, the Mac- 
millan Co., New York, 1906. 



NATURE AND SCOPE 5 

shall form a well-organised and therefore intelligible 
whole. From this point of view all Exposition is 
explanation or interpretation, though in order to com- 
plete the explanation it may be necessary to place the 
pupil in such a position that new matter may be as- 
similated. Sometimes the expositor can so arrange old 
matter that it becomes intelligible without the intro- 
duction of anything new, but frequently it happens 
that in the pupil's knowledge there is some link lack- 
ing, without which all the present material is necessa- 
rily unintelligible. To introduce the missing elements 
is clearly an essential part of Exposition. I have 
known a man who had a really excellent knowledge 
of French completely puzzled by a passage that pre- 
sented no apparent difficulty. He could make no sense 
out of it because he did not happen to know that 
Monsieur, when used absolutely, meant the eldest 
brother of the king of France. 

It is worth remarking that in this connection ^^ex- 
planation" has no reference to the ultimate meaning 
of the matter to be dealt with. It is not a metaphysical 
term. Accordingly, from the teacher's point of view. 
Exposition does not include the discovery of the true 
meaning of the matter to be expounded, but only the 
setting forth of that matter in such a way as to be in- 
telligible to the pupil. The facts and the explanation 
of the facts are for the teacher the data of Exposition. 
He may be misinformed about the materials he is deal- 
ing with, his facts may not be facts, his explanations 
of his facts may not stand the test of investigation, 
and yet his exposition may be excellent. As an ex- 
positor his business is so to present his facts that they 
shall carry with them the explanation that appeals to 



6 EXPOSITION AND ILLUSTRATION IN TEACHING 

him as satisfactory. Too often it has been assumed 
that an intelHgent mastery of the facts to be presented 
is enough to quahfy a teacher for his work/ In reahty 
it is no more than the essential condition of his begin- 
ning to learn to apply his art. For our present purpose 
we shall assume that the teacher has acquired the 
necessary facts and has mastered their meaning. The 
problem remains to communicate these facts so that 
they shall convey to the pupil the meaning the teacher 
has accepted as the true one. 

The teacher may not only adopt a wrong interpre- 
tation of the facts, but may know that his interpreta- 
tion is false, and yet be an excellent expositor. Pro- 
fessor J. W. Allen ^ provides an admirable illustration. 
Taking the Reformation as subject, he gives three sep- 
arate expositions of its meaning, one from the Roman 
Catholic point of view, another from the Protestant, 
while the third is written from the standpoint of a 
critical Mercutio who calls for "a, plague o' both your 
houses. '^ By appropriate overemphasis and com- 
pression, each of the accounts, while not inventing 
incidents or what are commonly called ^^facts,^' con- 
trives to convey an entirely different impression from 
the others. So far as each is successful, it leaves the 
mind of the pupil with his ideas of the Reformation 
reconstructed in a particular way, a way that was first 
developed in the mind of the expositor, though, as 
we see, he has adopted at least two other modes of 
reconstructing the available elements. 

^ Cf . De Quincey : " The t6 docendum, the thing to be taught, has 
availed to obscure or even to annihilate for their eyes every anxiety 
as to the mode of teaching." Essay on Style. Collected Writings 
(Masson, 1897), Vol. II, p. 160. 

2 The Place of History in Education, 1909, p. 210. 



NATURE AND SCOPE 7 

The test of the expositor is: does he produce on 
the mind of the pupil the impression he desires to pro- 
duce ? Literary style is sometimes tested by the clear- 
ness with which it conveys the author's meaning. But 
sometimes the author may not desire that his mean- 
ing should be understood. He may want his words to 
convey one meaning to one set of readers and another 
to another. From this point of view the test is: does 
he convey the meaning to each that he intended to 
convey ? Style is not so much a means of making an- 
other know what we think, as it is a means of producing 
a certain effect upon the mind of another. So in the 
case of the expositor, whether he be honest or dishonest, 
the result of successful exposition must be that there 
now exists in the mind of the hearer or reader a com- 
bination of mental elements that previously existed in 
the mind of the expositor. There may be many other 
ways in which the elements could be combined, and 
these possible combinations may all have been formed 
at one time or other in the mind of the expositor, but 
if he has succeeded in his present work, only one of these 
combinations is able to establish itself in the mind of 
the person he is dealing with. Exposition, therefore, 
comes to be, in the ultimate resort, the manipulation 
of the ideas of another. 

This gives a more definite meaning to the term ex- 
planation as used by the teacher. Some people do not 
see how things can be explained. They admit the ad- 
vantage of statement and demonstration, but cannot 
see how something that has been stated and demon- 
strated can be made clearer by writing or talking about 
it. They quote the case of the little girl who has won 
the good-will of all the teachers' common rooms in the 



8 EXPOSITION AND ILLUSTRATION IN TEACHING 

world by her protest that she thought she could under- 
stand her arithmetic if only her mother would give 
up explaining it/ In his Modern Painters, Ruskin 
tells us bluntly: ^^Explanations are wasted time. A 
man who can see, understands a touch; a man who 
cannot, misunderstands an oration." The contrast 
between a touch and an oration is not very happy, as 
it might be held to imply a comparison between two 
different kinds of explanation — practical and verbal. 
But even if we limit the contrast to the cognate terms, 
a word and an oration, we have still the implied admis- 
sion that the word has done some good. In actual ex- 
perience it is often found that only a word is needed to 
estabHsh the proper relation among a group of ideas that 
need nothing but the help of this word to reduce them- 
selves to a combination intelligible to a person who 
otherwise is unable to understand them. It is quite 
possible for a man to have in his mind all the facts 
necessary to explain something that he does not under- 
stand, and yet be quite unable to make the necessary 
application of his knowledge. The facts must be put 
in a certain order before the true relation can be seen, 
and it is the business of the expositor, by means of 
words or otherwise, to arrange them in this order. 

One of the great difficulties at certain examinations 
is to keep candidates from getting just this kind of 
help from each other. A difficult problem in Perspec- 
tive or in Orthographic Projection often becomes quite 
easy to a candidate from a single glance at his neigh- 

^ In his Charles Dickens, Mr. G. K. Chesterton says: Dickens "had 
one most unfortunate habit, a habit that often put him in the wrong, 
even when he happened to be in the right. He had an incurable 
habit of explaining himself." 



NATURE AND SCOPE 9 

bour's completed drawing, though without that glance 
he could make no sense out of the problem as stated in 
words on his examination paper. He has all the knowl- 
edge needed to work out the problem, but he lacks the 
power of making the initial combination. At a certain 
examination in Applied Mathematics an industrious 
but not very original student found herself unable to 
understand a particular question on her paper till she 
chanced to see a fellow-candidate twirling her finger in 
a particular way. The motion of the finger at once 
suggested the idea of a left-handed helix, and the point 
of the question became plain. Both candidates hap- 
pened to be considering the same problem at the time, 
but there was no intentional signalling. The clever 
candidate did not know that she had helped the other. 
It has to be remembered that unless the duller student 
had had the necessary materials in her mind, no amount 
of finger-twirling would have been of the slightest use 
to her. 

In a similar way an uninteUigent plumber has often 
in his mind all the facts that are necessary to the mas- 
tery of a difficult job in a house, and is yet unable to 
apply his knowledge. The householder makes several 
suggestions, most of them futile, but happens to hit 
upon one combination that appeals to the practical 
but unintelligent workman, who then exclaims, ^^Ah, 
now that you put it that way — , '^ and proceeds to 
carry out a suggestion that he could not originate. In 
a certain sense the ignorant householder has explained 
matters to the plumber. What the householder has 
done more or less by chance, the skilful expositor must 
do deliberately. 

Exposition may well be described as a bipolar pro- 



10 EXPOSITION AND ILLUSTRATION IN TEACHING 

cess. For our own ends we may regard it now from 
the point of view of the expositor, and now from that 
of the person to whom something is being expounded. 
But the process is working from both sides all the time. 
It is interesting to note that at the present moment 
psychologists are feeling keenly the need for double 
terms in the case of similar bipolar processes.^ In 
suggestion and imitation, for example, we have the 
two poles of the process and a term to describe only one 
of them. Suggester and imitator are words that stand 
for the persons who suggest or imitate; but we have no 
terms to denote those who are imitated or to whom 
suggestion is made. In the books we find rather clumsy 
references to the subject, the patient, the pattern, the 
model. Sometimes it is proposed to follow certain 
analogies and boldly introduce the two terms, suggestee 
and imitatee. But apart from the barbarous sound of 
expositee or expositatee, there is the serious objection 
that this form overemphasises the passive element. 
The person to whom an exposition is being made is to 
a certain extent more passive than is the expositor, 
but he is far from being quite passive. He is guided by 
the expositor, and to that extent plays a passive part, 
but if the exposition is to be successful, the person to 
whom the expositor appeals must bestir himself, and 
react vigorously on the material supplied by the ex- 
positor. 

In what follows we shall have to make constant 
reference to ^'the person to whom the exposition is to 
be made," and it is obvious that this cumbrous peri- 
phrasis cannot be repeated on every occasion. So 
with 'Hhe matter to be expounded." In both cases 

* Cf. Mr. W. Macdougall's Social Psychology, p. 325. 



NATURE AND SCOPE 11 

we require a technical term. With regard to the matter 
to be expounded, we seem to have a word to our hand. 
Sheltering under the authority of De Quincey's use of 
TO docendum, the thing to be taught, we would sug- 
gest the term expositandurrij the thing to be expounded. 
By dropping the Greek to we render the term a little 
less formidable, and lose nothing in the way of accuracy. 
We have seen that no such convenient term suggests 
itself for the person to whom the exposition is to be made. 
Probably it will be best to retain the ordinary word 
pupil. To be sure, the word is not commonly applied 
to a person who has left school, and we must in these 
pages apply it on occasion to people of quite mature 
years and high attainments; but no confusion need 
arise if we clearly understand that by pupil we shall 
in this book indicate the person who in the process of 
Exposition occupies the pole that is the correlate of the 
expositor-pole. After all, a learned professor receiv- 
ing instruction from a street urchin how to find his 
way back to his hotel is, for the time being, a pupil. 

Our first business in preparing this ordinary term 
pupil for our use is to get rid of the lingering notion that 
it represents a purely passive side of the process of 
learning. It connotes rather that the person is being 
directed in his activities than that he ceases to be active. 
We are prone to regard listening as in itself a passive 
matter. The audience is conspicuously passive, while 
the lecturer or preacher is as conspicuously active. 
Preaching has, in fact, been defined as '^an animated 
dialogue with one part left out." But this part that 
is left out as spoken word must certainly be suppHed 
as inner thought all through the sermon; else the 
preaching is a complete failure. The difference be- 



12 EXPOSITION AND ILLUSTRATION IN TEACHING 

tween teaching and lecturing lies just here. No fault 
is more common among inexperienced teachers than the 
tendency to do all the talking, and to treat the pupils 
as mere sleeping partners in the work of the class. 
'^Too much of a lecture'' is the hardest worked cliche 
in the Normal master's repertory of critical phrases/ 
In class work the one part must not be left out. There 
must be give and take ; the pupils must be allowed not 
only to be active, but to show their activity. In Ex- 
position the teacher may work either by the way of 
open dialectic, the rapid interchange of question and 
answer, or by the more sedate methods of the lecture. 
The important point to note is that the pupil must be 
equally active in either case. The psychology of listen- 
ing has not been sufficiently considered by teachers. 

To begin with, we are inclined to regard listening as 
more continuous than it really is. Psychologists are 
laying more and more stress on the rhythmic element 
in the phenomena in which they are interested. No- 
where is this rhythmic element more prominent than 
in listening, especially when long periods are considered. 
Trained listeners, such as students who have reached 
the postgraduate stage, are able to listen with a fair 
degree of continuity throughout an hour's discourse; 

^ It is interesting to note that in England the inevitable reaction 
has come. So thoroughly have students in training been drilled into 
a distrust of lecturing that they are now said to be losing the power of 
sustained speech. "Few of our recently trained teachers," says Pro- 
fessor Mark Wright, " can make a well-arranged verbal presentation to 
a class for ten minutes, without asking questions." It would certainly 
be a pity if teachers lost the power of consecutive presentation, but 
of the two the loss of this power of lecturing would be much less seri- 
ous than the loss of the power of conducting class work on the Hues 
of a vigorous dialectic. Fortunately, in America, there is little danger 
of the loss of sustained speech. 



NATURE AND SCOPE 13 

but your ordinary amateur listener, say the man who 
confines himself to a sermon a week and an occasional 
popular lecture, hears only in patches. Salient points in 
the discourse stand out, but each of these is a point of 
departure for trains of thought not bargained for by the 
speaker. The untrained listener rushes off from each 
salient point — and often from points that are not at 
all salient from the speaker's point of view — in a 
direction determined by the acquired content of his 
own mind, and he is recalled only by the emergence of 
another point in the lecture that catches his wandering 
attention. 

Fortunately, what is true in interstitial vision is true 
here. Just as the mind fills in a great many of the gaps 
that occur in actual vision, so it fills in a great many 
gaps that occur in the hearing of a discourse. Even 
dull people who are in earnest about the sermon go 
away with some fairly complete general idea of the 
whole (it is taken for granted that there is a general 
idea underlying the whole), but in many cases, no doubt, 
even after honest attention, the inexperienced listener 
goes away with only one or two prominent points, which 
are not by any means necessarily points in the main 
line ,of thought, but are more likely to be prominent 
points of illustration. 

A training in the art of listening is therefore an im- 
portant part of Exposition. Unless the expositor can 
assure himself that his pupils are doing their share of the 
work, he must be very doubtful about his success. In 
class-teaching he will, of course, seize every opportunity 
of making the pupils take an overt share in the work; 
but in the case of a more or less formal lecture this is 
difficult, sometimes, indeed, impossible; so the lecturer 



14 EXPOSITION AND ILLUSTRATION IN TEACHING 

must do what he can to encourage the pupils to test 
their powers of continuous attention. An excellent 
test that they can themselves apply is to see how far 
they can anticipate what is coming. Certain lecturers 
resent such a test. I have known one quite lose his 
temper when this matter was brought before him. He 
did not put it that way, but his view obviously was that 
nobody could anticipate what he was going to say in 
any of his lectures. But the test implies no challenge 
of the lecturer's originality. No doubt at the very 
beginning of an isolated lecture by an unknown person, 
one cannot usually anticipate what is coming, and, 
further, at many points in the lecture one may be quite 
unable to guess what is coming next. But in an ordi- 
nary lecture or sermon the experienced listener is gen- 
erally able to anticipate a great deal of what is com- 
ing. When a halting speaker hesitates for a word, 
there are usually scores of his hearers who have already 
supplied it. 

What the psychologist points out to us in our ordi- 
nary reading of a book or newspaper is true in our listen- 
ing. In almost every case the incidence of attention 
is not on the word that occupies the centre of the field 
of vision.^ So in music we are familiar with the fact 
that the performer's eye is frequently bars ahead of 
the note he is actually striking, and in certain familiar 
combinations the conclusion of a passage seems to come 
of its own accord, even when the notes are not seen at 

^ Dealing with reading aloud, Mr. E. V. Lucas, in The Avthor for 
July, 1909, writes the suggestive words: "Lacking the needful power 
of seeing two lines ahead (as John Roberts used to see two cannons 
ahead), I am continually falling into wrong stresses and misunder- 
standings, which annoy me like little stings." 



NATURE AND SCOPE 15 

all ; that is to say, certain common endings will be played 
quite naturally by the performer, even if the notes oc- 
(cur on the page that has not yet been exposed. We are 
too apt to assume that our reading and our listening 
•are matters of word by word understanding. Our 
thinking is not carried on in this atomistic way. We 
work with much bigger units than the individual word 
or sound. We can never know the present except in 
relation to the past and the future. In the stream 
of thoughts that pass through our minds the present 
thought is the darkest in the whole series : — 

"The knowledge of some other part of the stream, past or future, 
near or remote, is always mixed in with our knowledge of the 
present thing." ^ 

When Shakespeare and Shelley agree in selecting as 
man's high prerogative the power of ^ booking before 
and after," they are building on a sound psychological 
foundation. The present can be understood only by 
reference to the past and the future. 

In listening, the pupil should always be using the past 
to anticipate the future. The beginning and ending 
of good listening is anticipation — being able to project 
ourselves towards the point up to which the lecturer 
is leading. We may not be able to anticipate the lec- 
turer sentence by sentence. It may be that we are 
unable to complete such a sentence as '^The most op- 
timistic writer on Education is ." Here it is prob- 
able that very few could add the missing word in the 
sentence as it thus occurs out of the blue. But sup- 
pose this sentence occurs in the middle of a lecture, a 
good lecture — that is, a lecture that has been thought 

* W, James: Principles of Psychology, VoL I, p. 606. 



16 EXPOSITION AND ILLUSTRATION IN TEACHING 

out and organised — there would have been in all 
probability indications by the help of^ which an expe- 
rienced listener could infer at least the category under 
which the individual name is to be found. So far from 
being a reflection on the lecturer's originality, it is the 
highest compliment to him that his audience should 
be able to anticipate, within limits, what is coming. 
It is your careless, unprepared, unmethodical man who 
says the unexpected things. For remember, even with 
a professional dealer in paradoxes, it is quite possible, 
by the rule of contraries, or in extreme cases, when that 
rule fails, by the rule of contra-contraries, to anticipate 
what he is going to say. In other words, an organised 
lecture has a style underlying it that is all in the whole 
and all in every part, and that style can be surprised 
by a sympathetic listener. A merely capricious lecture, 
on the other hand, has nothing by which its develop- 
ment may be followed. 

Note further that the essential thing is not so much 
that the pupil is to be able to anticipate the very points 
to be raised, and how they will be settled, as that he 
must adopt the anticipative attitude. The pupil- 
mind must be feeling its own way into the problems 
that are being dealt with, and must keep on asking 
itself questions about the possibilities of the case. 
It may be thought that this stretching out of the mind 
towards what is to come will render it oblivious to what 
has gone before, that it will be so busy with the future 
as to lose sight of the past. On the contrary, it is only 
by relying upon the past that the mind has any chance 
of anticipating the future. The really active mind is 
playing all round the subject it is examining, and from 
what has been already presented, it gets all manner of 



NATURE AND SCOPE 17 

impulses urging it to make tentative advances in this 
direction and in that. Each advance is not only sug- 
gested by what has gone before, but must be tested 
by its consistency with the facts that have suggested it. 
Assuming that the ultimate purpose of Exposition 
is to cause to arise in the mind of the pupil a combina- 
tion of ideas exactly corresponding to a combination 
already formed in the mind of the expositor, it is clearly 
of the first importance to find out what means are at 
our disposal to bring about this combination in the 
pupil's mind. This demands a study of the nature of 
ideas and the laws according to which they act. But 
before entering upon details, it is well to get a general 
view of the whole ground. In ordinary language we 
use the word Illustration as meaning the clearing up 
of something that is in itself obscure. This idea we 
found to underlie also the meaning of Exposition. In 
point of fact, there is a certain confusion in the popular 
use of these two terms, a confusion that has a good deal 
to justify it in the usage of capable writers. Appealing, 
as in the case of the term Exposition, to the disinterested 
verdict of the dictionary, and, in order to widen our 
outlook, selecting an American lexicographer, we find 
that Webster thus delivers himself on the meanings of 
the verb to illustrate : — 

1. To make clear, bright, or luminous. 

2. To set in a clear light ; to exhibit distinctly or conspicuously. 

3. To make clear, intelligible, or apprehensible; to elucidate, 

explain, or exemplify, as by means of figures, comparisons, 
and examples. 

4. To adorn with pictures, as a book or subject; to elucidate 

with pictures, as a history or romance. 

5. To give renown or honor to ; to make illustrious ; to glorify. 

c 



18 EXPOSITION AND ILLUSTRATION IN TEACHING 

The first meaning is purely literal, as shown in the 
line quoted from Chapman: ^^Here when the moon 
illustrates all the sky," and does not interest us here. 
The fifth meaning is also foreign to our present purpose, 
and besides is obsolete. The fourth meaning embodies 
only a special form of illustration. But when we deal 
with the second and third meanings, we come to close 
quarters with the distinction between Exposition and 
Illustration. It is quite obvious that if we set some- 
thing in a clear light, or exhibit it distinctly or conspicu- 
ously, we are really doing what we have included under 
the head of demonstration when treating of Exposition. 
In the third meaning the overlap between the two 
processes becomes particularly noticeable. The pur- 
pose of Exposition is just to make things clear, intel- 
ligible, or apprehensible; but the differentia may be 
found in the second part, ^Ho elucidate, explain, or ex- 
•emplify, as hy means of figures, comparisons, and ex- 
(amples.^^ Here we are led to see that Illustration is 
to be regarded as a branch of Exposition. A mere 
setting forth of principles may be fairly called Expo- 
sition, but could not be justly called Illustration. It 
is only when we proceed to supply examples, and to 
institute comparisons, or in some other way to elabo- 
rate our presentation, that we can be said to illus- 
trate. 

The secondary meaning, then, of Illustration, as 
found in the dictionary, but the primary meaning for 
our purposes, may be said to be the process of throwing 
light upon something that is assumed to be known 
already in a vague and more or less unsatisfactory way. 
There is always a principle or body of principles that 
may be regarded as given (though not, perhaps, neces- 



NATURE AND SCOPE 19 

sarily given to the pupil at the beginning of the illustra- 
tive process), and as thus forming the datum of the 
problem of Illustration. This I should like the reader 
to permit me to call the illustrandum as a parallel tech- 
nical term to the expositandum. One part of the func- 
tion of Exposition we have seen is to present new 
matter, and another is the manipulation of matter that 
has been already presented. One is tempted to limit 
Exposition to the first function and to hand over all 
the rest to Illustration. Anything that we do or say 
to introduce a different arrangement of ideas already 
in the mind of the pupil would on this view be properly 
called Illustration. We are not to lose sight of the fact 
that Illustration is a branch of Exposition, and must 
not be surprised to find a certain overlapping in respect 
of the matters treated. In point of fact, both processes 
deal with both the new and the old. Yet there is a 
difference in their use of the two kinds of materials. 
The new ideas introduced by Exposition form an es- 
sential part of the subject-matter that is under discus- 
sion, while the new matter introduced by way of Illus- 
tration may have only a secondary connection with 
the subject-matter. An illustration may introduce 
new ideas, but these are not in this connection treated 
as of importance in themselves, but only as throwing 
light upon the ideas that are at the time being ex- 
pounded. When Mill states in his second canon — 

"If an instance in which the phenomenon under investigation 
occurs, and an instance in which it does not occur, have every 
circumstance in common save one, that one occurring only in the 
former, the circumstance in which alone the two instances differ is 
the effect, or the cause, or an indispensable part of the cause, of 
the phenomenon " — 



20 EXPOSITION AND ILLUSTRATION IN TEACHING 

he is expounding; but he proceeds to illustrate when 
he goes on to say : — 

"li ABC, ADE, AFG are all equally followed by a, then a 
is an invariable consequent of A. li abc, ade, afg slW number 
A among their antecedents, then A is connected as an antecedent, 
by some invariable law, with a." ^ 

So far Mill can hardly be said to have introduced any 
new ideas by way of illustration. The letters are mere 
pegs ready to hang matter on when it is presented. 
When, in the following chapter of his Logic, he intro- 
duces a discussion of how '^arsenious acid and the salts 
of lead, bismuth, copper, and mercury" act as poisons, 
he is still illustrating the canon, but he is introducing 
a whole series of entirely fresh ideas that have no con- 
nection in themselves with the subject-matter under 
consideration, which is the logic of experimental method. 
In point of fact, he assumes that his readers know 
enough about chemistry to follow easilj^ his references 
to Baron Liebig^s theories. As a general rule it is 
unwise to use as illustrative material something that is 
very unfamiliar to the pupil. It is seldom good policy 
to use many new ideas in an illustration. In certain 
cases it may be justifiable to '^work up" an elaborate 
illustration out of new materials. But this is permis- 
sible only when it is possible to group into one mass a 
number of facts that are useful not merely as illustra- 
tive of certain points, but as themselves important 
elements in the organised whole that makes up the 
subject under consideration. Illustration will thus be 
seen to be, on the whole, rather a work of arrange- 
ment than of addition. 

1 Logic, Book III, Chap. VIII. 



NATURE AND SCOPE 21 

All the same, it is clear that illustrations of the na- 
ture of those submitted by Mill from Baron Liebig 
cannot but convey in passing a certain amount of new 
information. Not only do they make clearer and more 
definite the points that they illustrate, but they in- 
crease the mental content of the pupil. He may not 
know the principle of the lever any more accurately 
after a long series of illustrative examples, for it is 
quite possible to understand the principle from only 
one example, but he will understand it in a broader 
way. His experience has been enriched by the number 
of cases in which he has seen the principle exemplified. 
He does not know it more accurately, but he knows 
it more usefully. 

Hitherto we have been considering Illustration 
merely from the cognitive side, as a means to enable 
the pupil to understand something that is difficult. 
But our object is not always to make another under- 
stand something. It may be to make him realise more 
vividly, to appreciate, to enjoy. We must, therefore, 
make provision for the aesthetic use of Illustration. 
The importance of this aspect must not be underes- 
timated. An old clergyman, addressing an audience 
of beginners in his own profession, told them that they 
might preach over and over the same sermon at rea- 
sonable intervals, if only they took the precaution to 
change the text, and the illustrations.^ The congre- 
gation will remember the illustrations long after the 
expositions, the descriptions, and the exhortations 

* It is worth noting that young clergymen have complained that 
this gracious permission to use old sermons is no great relief. After 
all, they say, it is the illustrations that count, and if one has to work 
them up into the very warp and woof of the sermon, this practically 
means that the sermon has to be rewritten. 



22 EXPOSITION AND ILLUSTRATION IN TEACHING 

have been comfortably forgotten. Herein lies one of 
the chief dangers in the use of Illustration. There is a 
strong temptation to use it for the sake of its own 
intrinsic interest, instead of for the interest it arouses 
in connection with the subject under discussion. Un- 
less an illustration forms part of the very nature of a 
lesson, unless it is worked into the very warp and woof 
of the whole, it is illegitimate.^ An illustration must 
not be used as a sedative. Its function is to stimulate. 
The teacher may think that he is entitled to introduce 
a story to brighten up a dull lesson. But he can pur- 
chase this privilege only by inventing a connection 
between the story and the lesson he is teaching. Some 
of the old English essayists supply capital examples 
of this justifiable combination of the didactic and aes- 
thetic functions of Illustration. Thomas Fuller, for in- 
stance, makes a very systematic application of this 
form. He has a habit of marking off his essays into 
short paragraphs, each beginning with an easily under- 
stood generalisation immediately followed by one or 
more illustrations that give it point. Thus, in his es- 
say, ^'Of Memory," we have the fourth paragraph 
running : — 

"Overburthen not thy memory to make of so faithful a servant 
a slave. Remember, Atlas was weary. Have as much reason as a 

^ People who make a study of the art of advertising take the view 
that the main purpose of illustration in a newspaper or on a poster 
is to attract attention. The drawing may be bad ; it may not accu- 
rately represent the object advertised, but if it catches the attention 
of the passer-by or the indifferent newspaper reader, it has served its 
purpose: "Charles Austin Bates, the most successful advertisement 
designer of the day, has repeatedly asserted that the function of the 
illustrator is to attract attention, and not necessarily to illustrate." 
Illustrated Advertising, by F. W. Johnston, Ninth Edition, Toronto. 
1901. (Introduction.) 



NATURE AND SCOPE 23 

Camel, to rise when thou hast thy full load. Memory, like a purse, 
if it be overfull that it cannot shut, all will drop out of it. Take 
heed of a gluttonous curiosity to feed on many things, lest the greedi- 
ness of the appetite of thy memory spoil the digestion thereof. 
Beza's case was peculiar and memorable; being above fourscore 
years of age, he perfectly could say by heart any Greek chapter in 
St. Paul's Epistles, or anything else which he had learned long before, 
but forgot whatsoever was newly told him ; his memory, like an inn, 
retaining old guests, but having no room to entertain new.'' 

This use of Illustration, common in Bacon, and in a 
less condensed form in modern essayists, is valuable 
in sermons and hortatory addresses, but must be used 
sparingly in lectures, and more sparingly still in les- 
sons. 

Essayists who follow more or less the method of 
Fuller are read largely for the interest of the illustra- 
tions. But, after all, the best essayists do make their 
generalisations the important points. All the rest of 
the matter centres round them. The illustrations may 
not be necessary to make clear the actual meaning of 
the thesis, but they at least illustrate. They form an 
organic part of the whole; they are not dragged in 
merely for the sake of their intrinsic interest. In a well- 
organised lecture or lesson it is possible that the illus- 
trations may occupy more space than the statements 
to be illustrated; but the main statements are felt to 
be the essential matters; the illustrations, however 
numerous, are organically interstitial. On the other 
hand, there are lectures and lessons, and even books, 
in which the illustrations are the main element, and the 
rest of the matter is worked in around them. The 
generalisations are interstitial; the substantive mat- 
ter is made up of what are nominally illustrations. 
Lectures on ''The Humour of Mark Twain," on ''The 



24 EXPOSITION AND ILLUSTRATION IN TEACHING 

Blunders of School Children/' on '^Election Time in 
Texas/ ^ are all very likely to turn out to be series of 
illustrations with a few strenuously invented general- 
isations keeping them apart. The most popular form 
of book review is made-up mainly of interstitial matter, 
and lantern lectures have an almost irresistible ten- 
dency to resolve themselves into interstitial common- 
places that only a good set of slides can condone in the 
judgment of an intelligent audience. 

Some teachers may reasonably interpose here, and 
maintain that lantern lectures ought to be interstitial. 
There is a great deal to be said in favour of such a view. 
But to adopt it would be to change the standpoint 
from which we have been considering the whole matter. 
It is quite reasonable to maintain that the most valu- 
able part of a lantern lecture is not what the lecturer 
says, but what his slides show. Still, if the information 
conveyed by the slides is regarded as the primary 
matter, they can no longer be treated as illustrations: 
they have become the substantive matter of teaching. 
The interstitial remarks of the lecturer are really illus- 
trative of the slides. In the case of a literary lecture 
professing to give a critical estimate of a writer's works, 
it is illegitimate to depend for the main interest of the 
lecture on the intrinsic attraction of the quotations. 
The interest should be in the relation the lecturer is 
able to establish between his generalisations and the 
particular quotations that he uses to support his views. 
'^Note the beauty of this passage;" '^What could be 
more inspiring than the following;" ''If you wish to 
know what pathos means, turn with me to the Ode to 
;" ''No one with a spark of humour in his compo- 
sition could refrain from chortling over the exquisite 



NATURE AND SCOPE 25 

passage I am about to read to you;" all these are 
mere bits of padding that mark what may be called 
finger-post criticism. On the other hand, some of the 
finest passages of Shakespeare may be read with almost 
no interest in their primary meaning because they are 
being used to illustrate a point in the Shakespeare- 
Bacon controversy. It is quite possible for a lantern 
lecture to depend on the actual lecture that is delivered, 
so that the hearers recognise that the slides, however 
good they may be, would either have been meaning- 
less without the lecturer^s exposition^ or would have 
had quite a different meaning from that they actually 
took under his manipulation. 

It is clearly important for the teacher to distinguish 
between the values of certain materials as illustrations, 
on the one hand, and as the subject of actual teaching 
on the other. Finger-post criticism has its place in 
school. Indeed, it is probable that some readers of this 
chapter have got rather angry at the idea of spoiling 
Shakespeare by using his writings merely to illustrate 
an argument. But for our professional purposes it is 
important to keep apart the two uses of subject-matter, 
the one as illustration, the other as substantive matter 
of instruction. It is an excellent thing to read to a class 
a series of extracts from a standard author with only 
a few explanatory comments — probably a better thing 
for the class than to give it a seriously worked-out 
lecture in which only illustrative extracts are given. 
We have to remember that the purpose in the two cases 
is different. In the first we are giving the pupil the 
actual material; in the second we are entitled to as- 
sume that the pupil has the material, and all that we 
have to do is to manipulate that material in such a way 



26 EXPOSITION AND ILLUSTRATION IN TEACHING 

as to enable him to acquire a better mastery of what 
he already possesses. Under ideal conditions in a lec- 
ture on the Humour of Tom Hood it may be assumed 
that the audience have all read Hood's works at least 
once. The lecturer has therefore no need to fall back 
on mere finger-post criticism; and on the other hand, 
he has no temptation to rely upon the intrinsic interest 
of the passages he quotes. In practice, however, it is 
impossible to attain the ideal, so the teacher has to 
combine in the most effective way he can the two uses 
of his material. In a lesson intended to deal with liter- 
ature as subject-matter, the teacher should seek to 
make himself as little prominent as possible. The 
matter is the important thing. So long as lantern slides 
are used as teaching matter (docendum), the pupils are 
entitled to attend to the teacher's explanations only 
so far as they feel the need of them. When the slides 
are used as illustrations, the incidence of attention 
should be reversed. 

The subject-matter of teaching illustrations is of con- 
siderable importance. In certain branches no problem 
emerges. Only one kind of illustration is possible, and 
the choice of the best material in that kind is really an 
essential part of the specialist's knowledge of how to 
teach his subject. But in many subjects illustrations 
may be sought from all parts of the field of knowledge, 
and the question arises whether it is better to select 
illustrations from matter that is cognate with that 
the pupils are dealing with, or to choose matter as 
different from that as possible. Generally speaking, 
it is better to keep to cognate subjects, as in this way 
the teacher may be teaching one branch substantively 
while illustrating another. On the other hand, there 



NATURE AND SCOPE 27 

is the danger of weariness if the pupils are never allowed 
a change of venue. Teachers are beginning to realise, 
what pupils have realised some time ago, that it is 
possible to carry the method of correlation to such an 
extent as to exhaust all possible interest in certain 
matters. Illustrating in a circle is not quite so deadly 
as reasoning in a circle, but it has its serious defects. 

From what has gone before, it might appear to follow 
that in using Illustration we must always adopt the 
deductive method. The illustrandum is given as a sort 
of general statement, which the rest of the process 
works out and applies, as in ordinary deduction. But 
Illustration may sometimes be used in what may be 
fairly called an inductive way. Indeed, the methods 
used in applying Illustration vary between two ex- 
tremes. At the one end is the plan of depending 
mainly upon Exposition. Everything is stated in the 
plainest possible terms, and illustrations are introduced 
only where absolutely necessary, and are always stated 
to be illustrations. They are formally introduced by 
as, or some such word, or are actually named illustration 
or example. This all fits in with the deductive notion. 
At the other extreme are found those cases where the 
illustration is given almost without comment, and its 
meaning left to be inferred. Especially when many 
illustrations are given and the pupil is led to draw cer- 
tain inevitable conclusions, the resemblance to induc- 
tion is so great that the reader may not unnaturally say 
that it is induction and nothing else. The genders of 
Latin nouns, as gathered from inspection of their mere 
form, may be inculcated by a series of exercises to our 
pupils in which certain typical Latin nouns are system- 
atically called into play without any overt reference 



28 EXPOSITION AND ILLUSTRATION IN TEACHING 

to their gender. But some may be inclined to question 
whether this is really Illustration. Is it not a process 
in which we teach rather than merely illustrate ? It is 
true that the illustrandum does not appear till the 
process is completed, but it has been in the teacher's 
mind throughout. It may not, therefore, be altogether 
unreasonable to regard the process as one of Illustra- 
tion, the teacher adopting the deductive attitude and 
passing from the generalisation to the particulars, and 
the pupils reversing this order. This view is worth 
elaborating a little, as it is not quite in harmony 
with the usual nomenclature. 

Sometimes, in ordinary experience, light is thrown 
upon some matter that nevertheless cannot be called 
the illustrandum, since, at the beginning, it is not pres- 
ent as such in the mind of either the pupil or the 
teacher. A person who knew no German was called 
upon to make a vocabulary that included over two 
thousand German nouns. She had to indicate in each 
case the gender, the genitive, and the meaning of the 
noun. Her method was the straightforward one of 
looking up each word in a standard German dictionary, 
and copying out the relevant details. As the work 
progressed, she found that she could anticipate with 
increasing accuracy the gender and genitive of each 
new noun as it presented itself; till towards the end 
she was strongly tempted to depend upon her general 
impression, without troubling to verify it by reference 
to the dictionary. 

A still more striking case is one that occurred under 
the deplorably bad system of payment by results, that 
used to obtain in England, in which the teacher's pro- 
fessional reputation depended upon the percentage of 



NATURE AND SCOPE 29 

pupils he could contrive to squeeze through certain 
individual examination tests at the end of each school 
year. A harassed teacher, who had not enough time to 
attend to the dullards that under this system were the 
persons of chief importance, tried to get rid of the 
troublesome clever pupils in her youngest class by keep- 
ing them busy with long addition sums, while she de- 
voted all her energy to getting her dullards to work 
little sums with sufficient accuracy to obtain the coveted 
pass. Through much practice the clever pupils were 
able to work the long sums so rapidly that they were 
continually worrying the poor teacher by coming back 
for more. To save time in giving out fresh sums, she 
dictated only one line, say 987,526, and told the pupils 
to repeat that line on their slates another eight times, 
making nine lines in all, and then add the whole. The 
remarkable thing was that after some weeks of this in- 
genious labour-saving device, the poor teacher was more 
harassed than ever. The children appeared to have 
acquired a positively uncanny speed in addition. On 
investigation it was found that the pupils had gradually 
noticed that there was something peculiarly sym- 
metrical about the new sums the teacher was giving 
them. Some of the more intelligent among them began 
to see that it was a pity to waste time adding up a 
column of nine eights when they had added up such a 
column a little while ago. They began, therefore, to 
keep a note of results for future use, and gradually 
gave up adding at all, except in the matter of carrying 
from one column to another. The step from this to 
pure multiplication was easy, but as a matter of fact 
was not made by the pupils themselves; the secret of 
multiplication was communicated to them (for a con- 



30 EXPOSITION AND ILLUSTRATION IN TEACHING 

sideration) by certain pupils in higher classes to whom 
the young experimenters had been talking about the 
peculiar sums they had lately been having. The net 
result was that those pupils learnt in a few weeks, and 
with great satisfaction, the full meaning of the multi- 
plication table and its application, matters that under 
ordinary circumstances take a whole school year to 
master. 

It might be argued that in these two cases the 
pupil passed from the illustration to the illustran- 
dum. But this is an unnecessary strain on the terms. 
It is better to restrict the term Illustration to those cases 
in which there is a deliberate attempt to throw light 
upon a given subject. Here, to be sure, light was 
thrown upon certain matters, but without any delib- 
erate intention on the part of either teacher or pupil. 
The learning, in fact, was carried on in the ordinary 
inductive way. 

The case is somewhat different when the teacher 
makes a deliberate use of the illustration before pre- 
senting the illustrandum. He is often able to arrange 
matters so that certain experiences of school difficulties 
that must occur at any rate among his pupils shall 
occur at certain stages that are convenient for him. 
He can, in short, modify the order of the development 
of the pupil's mental experience in such a way that the 
elements of this experience shall form certain combi- 
nations that from the point of view of the school are 
desirable because they lead to the pupil's coming to 
certain desired conclusions. To put it somewhat less 
abstractly, it is quite possible for a master who has 
taught the same school grade for several years to know 
very exactly how certain of the special points to be 



NATURE AND SCOPE 31 

dealt with in that grade will affect certain minds. 
He is therefore in a position to arrange the matters to 
be presented in the order he thinks will best aid their 
proper assimilation. For example, the construction 
of the accusative with the infinitive in Latin involves 
problems for the young mind that are insoluble at cer- 
tain stages of knowledge. This subject may be illus- 
trated in advance by a carefully arranged series of 
lessons that have no apparent connection with the 
oratio ohliqua, as found in Latin. English grammar 
may be so taught as to pave the way, and even the use 
of brackets in algebra may be regarded as a prepara- 
tion, — as may be seen in the interesting little mono- 
graph on the subject by the Rev. J. H. Raven.^ 

In the ordinary sense of the term an illustration is 
expected to accompany the subject-matter to be illus- 
trated, so it must be admitted to be a little strain on 
the term to call such processes as those we have dealt 
with in the last paragraph Anticipatory Illustration. 
To be sure, the teacher always has the illustrandum 
before him as he prepares the exercises that are to throw 
light upon difficulties that have not yet arisen in the 
pupil's mind, and this gives a certain amount of justi- 
fication for the introduction of the term Anticipatory 

^ " Do the two accusatives both feel the influence of the Transitive 
dicit, and so form a complex noun, governed by dicit, so that the 
analysis will be : He mentions the-enemy' s-coming f Key (Lat. Gram., 
§ 911) seems to take a somewhat similar view to this. In analysing 
Ferunt Ccesarem rediisse, he has this original note : ' A mathematician 
might have expressed this by — Ferunt {Ccesar rediit)em, attaching 
the symbol of the accusative case to the clause. As the Romans 
were afraid to do this, adopting what under the circumstances was 
perhaps the best makeshift, they selected for the addition of the 
suffix the chief substantive.'" — Latin Exercises in the Oratio Ohliqua, 
by the Rev. J. H. Raven, p. 55. 



32 EXPOSITION AND ILLUSTRATION IN TEACHING 

Illustration. But the real reason for seeking to use 
the phrase is that there is need for some term to desig- 
nate a process whose importance is now beginning to be 
appreciated in schools. Using Anticipatory Illustra- 
tion in such a way that pupils must reach certain gener- 
alisations, may be regarded as a form of inductive teach- 
ing. The pupil may be so fed with illustrative matter 
that he is practically coerced into reaching certain con- 
clusions. The heuristic method, in its healthier forms, 
is nothing more than a system of Anticipatory Illus- 
tration inevitably leading to a conclusion that already 
exists in the teacher's mind. It is a caricature of the 
method to describe it as a process of placing the pupils 
in the position of the original discoverer of a certain 
truth, and keeping them there till they discover it for 
themselves. We cannot put pupils in the position of 
the original discoverer. We can turn them loose in an 
orchard and let them watch the apples falling; but it 
would be difficult to say how much time we should give 
them before we come back to find them in possession 
of the theory of gravitation. The teacher on the heu- 
ristic method never lets go the guiding reins. He may 
hold them now loose and now tight, but he never drops 
them. He knows the course and he keeps his pupils 
in it — with the minimum amount of restraint, it is 
true, but the restraint is none the less real. It is, 
throughout, a system of Anticipatory Illustration. 

It is sometimes maintained that the heuristic method 
gives no real training in induction, since all the matter 
is so carefully arranged beforehand that the mind is 
not left free. But the mind, as a matter of fact, is, 
under no circumstances, ever left free. It must react 
upon what is presented to it, and it acts in the same 



NATURE AND SCOPE 33 

way upon the material presented, whether that comes 
at haphazard or is carefully arranged in a definite order. 
The induction a pupil makes as the result of considering 
a number of anticipatory illustrations is as genuine as 
one that he makes in his ordinary experience. The 
fact that his ordinary induction is so often wrong, 
because the matter is not presented in a helpful order, 
is surely no advantage. So far as the intellectual pro- 
cess is concerned, there is no difference in the two cases. 
An induction either is an induction or it is not. 

A more plausible objection is that Anticipatory Illus- 
tration may be so arranged as to prevent the possibil- 
ity of error, and thus deprive the pupil of that prac- 
tice in dealing with deceptive cases that is so necessary 
as a preparation for the work of life. But here it is 
only necessary to remark that, in spite of the teacher's 
best endeavours, he will find it almost impossible to ar- 
range his anticipatory illustrations so that there is no 
loophole for error. Further, at later stages, the pupil 
is left more and more to his own resources. Under any 
system inductions must be verified, and this verifica- 
tion may be as well taught in connection with the 
heuristic method as with any other. All the needful 
precautions can be applied here as elsewhere. h 

As an example of the application of Anticipatory 
Illustration with the minimum possibility of error, 
take the case of teaching Euler's Theorem, that gives 
the formulae for the number of faces, corners, and edges 
of a pyramid or prism having a given geometrical figure 
as base. The data of the theorem may be so presented 
that the pupils must discover it for themselves. They 
are assumed to know what is meant by a face, a cor- 
ner and an edge. The teacher supplies the pupils with 



84 EXPOSITION AND ILLUSTRATION IN TEACHING 

the sixteen solids named in the following table, but the 
numbers as they appear on the printed table are not 
inserted : — 

EULER'S THEOREM 



Pyramids 


Name op Solid 


Prisms 


Faces 


Corners 


Edges 


Faces 


Corners 


Edges 


4 
5 
6 
7 
8 
9 
10 
11 


4 
5 
6 
7 
8 
9 
10 
11 


6 
8 
10 
12 
14 
16 
18 
20 


Triangular 

Square 

Pentagonal 

Hexagonal 

Heptagonal 

Octagonal 

Nonagonal 

Decagonal 


5 

6 

7 

8 

9 

10 

11 

12 


6 
8 
10 
12 
14 
16 
18 
20 


9 
12 
15 

18 
21 
24 
27 
30 


n + 1 


n + 1 


2n 


n-gonal 


n +2 


2n 


3n 



Provided with this blank table and the necessary 
solids, the pupil is called upon to fill in the required 
numbers by the simple process of counting from the 
actual solids the number of faces, corners, and edges. 
All he is asked to do is to fill up the table as far as the 
decagonal solids. Naturally the generalised expres- 
sions in terms of n that occur at the end of the table 
are not even suggested to the pupil. It is the purpose 
of the lesson to lead the pupils to reach the generalisa- 
tions in n for themselves. To enunciate these at the 
beginning of the lesson would be what Professor Henry 
E. Armstrong calls *' criminal.'' ^ 

At first the pupils fill up the table in that conscien- 
tiously indifferent way that children have of dealing 
with easy routine exercises. By and by they begin to 

* The Teaching of Scientific Method, p. 254. 



NATURE AND SCOPE 35 

note a certain symmetry, and their intellectual interest 
is aroused. It is an excellent plan to omit two of the 
figures, say the octagonal pyramid and the nonagonal 
prism, and invite the pupils to fill up the corresponding 
spaces by calculation. It will be found that fully half 
of the class will be able to do this directly they come 
to the place of the missing figure, and almost all the 
rest of the class will be able to fill in the blanks after 
they have completed the entries so far as they have 
solid figures to count from. 

The second stage consists in requiring the pupils to 
continue the table, filling in the non-technical terms 
in the name column, 11-gonal, 12-gonal, 13-gonal, 
and so forth down to 20-gonal. Experience showed 
that almost every pupil in a class of sixty boys of ten 
years of age could complete the table up to 20, and all 
this without one single word of explanation from the 
time the first number was set down till the 60 edges of 
the 20-gonal prism were recorded. 

Keeping to the case of the class just mentioned, 
the third stage consisted in setting the pupils to fill up 
the figures for a 40-gonal figure, then for a 60-gonal, 
then for a 100-gonal solid. Here there was a bigger 
percentage of breakdowns, and the method adopted was 
to write the correct line of figures on the blackboard 
after each solid had been attempted. In this way 
those who failed in the 40 solid saw how things 
went, and generally succeeded with the 60 or the 
100 solid. 

The fourth stage consisted in a series of exercises 
such as : How many edges has a 45-gonal pyramid ? 
a 45-gonal prism ? How many corners has a 72-gonal 
prism ? The correct answer was in each case placed 



36 EXPOSITION AND ILLUSTRATION IN TEACHING 

upon the board, and the pupils were thus enabled to 
correct any miscalculation. 

The fifth stage consisted in exercises that worked 
backwards: A ?-gonal solid pyramid has 41 corners ; 
how many faces has it? How many edges? What 
-gonal is it ? (That is, what number should go before 
the -gonal in the name column ?) 

The final stage consisted in an invitation to fill up 
the n-gonal figures. All that was explained was that 
n stood for any number, and that what was to be noted 
was whether the different numbers would be greater or 
less than n, and by how much. At the first exercise 
thirty-five boys wrote down the correct generalised 
form. They had won their generalisation. 



CHAPTER II 

Mental Content 

Teachers are now familiar with the phenomena of 
apperception. At the earhest stages pure sensation is 
possible to the developing human being, but very soon 
sensations are associated with meaning and become 
perceptions. Thereafter every stimulus that the mind 
has to deal with is modified by the results of previous 
stimulations. When we reach the plane of ideas, it is 
found that while every new idea presented is acted upon 
in accordance with the laws of mind, these laws can 
only be applied as conditioned by the other ideas at 
that time possessed by the mind. In other words, each 
new idea is acted upon by all the other ideas at that time 
available in the mind in question. This process is 
known as apperception. A given mind possessed of 
certain ideas must react in a determinate way when a 
given new idea is presented to it. Any one therefore 
who knows the general laws of mental activity and the 
content of a given mind may act upon that mind with 
a fair chance of being able to produce a desired mental 
result. In point of fact this is what the expositor does, 
for Exposition may be regarded as the process of guid- 
ing and directing apperception in another mind. 

The first assumption, then, underlying the art of 
Exposition is that it is possible for one mind to act 
upon another. Successful exposition implies that one 

37 



38 EXPOSITION AND ILLUSTRATION IN TEACHING 

mind has been able to produce a predetermined effect 
upon another. Now while our ordinary experience 
leads us to believe that this interaction between minds 
is continually going on, the slightest dip beneath the 
surface shows us that the matter is not nearly so simple 
as it appears. There is no direct communication 
between minds. Mind understands mind only by 
an elaborate system of interpretation. Philosophers 
puzzle themselves and their readers over the problem of 
the relation between the individual consciousness and 
what they call the general consciousness. But what- 
ever this relation may be it is one that does not admit 
of articulate expression. For all practical purposes 
each individual consciousness is insulated from every 
other. Consciousness is as impenetrable as matter: 
by no possibility can we penetrate into the conscious- 
ness of another. What goes on in that other conscious- 
ness can be understood by us only as the result of a 
process of inference from our own experience. The 
everyday act of influencing the mind of another, there- 
fore, acquires all the interest of a mystery. 

We may never be able to explain fully all that under- 
lies this mystery, but we can at least lay down certain 
conditions that must be complied with if we are to 
succeed in producing upon the mind of another a pre- 
determined effect. To begin with, we must be able to 
catch and retain the attention of the pupil. Next 
we have to acquire the power of manipulating his men- 
tal content so that there shall arise in his mind a com- 
bination of elements similar to a certain combination 
already existing in our own mind. To do this we must 
have a knowledge of the mental content of the pupil. 
The next condition of successful exposition is a knowl- 



MENTAL CONTENT 39 

edge of the laws according to which mind in general 
acts. No doubt there are great varieties in the de- 
tailed working of individual minds, but there are cer- 
tain laws which are of a very general character, it is 
true, but which within the wide limits of their applica- 
tion are absolute. We cannot break these laws even 
if we try; it is according to these laws that the mind 
always reacts upon material presented to it. They 
are generally known as the Laws of Thought as Thought, 
and are more frequently found in books on Logic than 
in books on Psychology. So exceedingly general are 
they, that when they are stated, they sound particularly 
empty. But it has to be remembered that their empti- 
ness is the result of their universality. They run as 
follows: The first, known as the Law of Identity, 
is represented by the enlightening formula A is A. 
This again is explained to mean that everything is 
equal to itself, or the whole is equal to the sum of the 
parts. It has to be noted that this statement has noth- 
ing to do with either the whole or the parts, except in 
their relations as whole and parts. It is found to be 
an imperative law of our thinking that we shall, under 
no circumstances whatever, conceive the whole as 
being either more or less than the sum of the parts. 
Of the many meanings that have been given to the 
Principle of Identity perhaps the one most in point here 
is that supported by F. H. Bradley. This is that under 
identical circumstances the mind must reaffirm what 
it has once affirmed. For example, if I have once truly 
said that the sky is blue, I am bound to maintain the 
affirmation, even though the sky, as a matter of fact, is 
blue no longer. ^^Once true, always true; once false, 
always false." ^ 

^ The Principles of Logic, p. 133. 



40 EXPOSITION AND ILLUSTRATION IN TEACHING 

The Law of Non-contradiction is the second of these 
momentous laws. This is expressed in the formula: 
What is contradictory is unthinkable. Its shortened 
form is A = not-A = 0, or A - A == 0. To take a 
concrete case, a watch cannot be both correct and in- 
correct at the same moment, and tested by the same 
standard, A person cannot be at the same time guilty 
and not guilty. 

The third law introduces us to what is known as the 
Excluded Third, or the Excluded Middle. This com- 
pels us to think that of two repugnant notions that can- 
not both coexist, one or the other does exist. '^Of 
contradictory attributions we can only affirm one of a 
thing; and if one be explicitly affirmed, the other is 
implicitly denied. A either is or is not. A either is or 
is not BJ^ ^ A centaur either is or is not. Socrates 
either is or is not guilty. 

From our present point of view the fourth law is of 
less consequence than the others. It is known as the 
Law of Sufficient Reason, and limits itself to the asser- 
tion that we must infer nothing without a cause, or 
rather without a ground or reason, as cause is usually 
restricted to the region of the actual, and reason to that 
of thought. The very statement of this distinction is 
an explanation of the comparative unimportance of 
this law as illustrating the ultimate process of thought. 
The nature and origin of the idea of causation has been 
elaborately discussed, and when so much can be said 
in favour of the Associational origin of the idea of Causa- 
tion, it cannot be maintained that this law has the cer- 
tainty that marks the others. 

So unassailable are these three laws that the general 

^ Sir William Hamilton : Lectures, Vol. Ill, p. 83. 



MENTAL CONTENT 41 

feeling of every one who hears them for the first time 
is that they are superfluous, if not indeed a little silly. 
Why state them so ponderously when no one questions 
their truth. Are we any further forward when we have 
admitted that A is A, that A cannot be both A and not 
A, that a thing must be either A or not A? Yet it is 
because of our unanimity on these apparently unim- 
portant points that we are able to reason with one 
another in the full assurance that we shall come to 
certain inevitable conclusions, if only the facts are 
stated aright. Two minds that are given the same facts 
cannot but come to the same conclusion. Depending 
upon these laws, we are able to rely upon producing by 
our exposition a definite calculable effect upon the 
minds of others. Given certain facts, we can prophesy 
the mind's reaction upon them. 

Unfortunately the certainty of reaction is disturbed 
by the nature of the facts submitted to the mind. 
When dealing with quite abstract elements, as in formal 
logic and pure mathematics, the action of the mind 
can be depended upon. But unfortunately the greater 
part of our mental activity is carried on in connection 
with matters that are far from abstract. It is custom- 
ary to use a figure of speech and speak, as we have done 
once or twice already, of mental content. Naturally 
we must be on our guard against accepting this figure 
as expressing literal truth. The relation between the 
mind and mental content is not that between container 
and thing contained. For convenience of expression 
we speak of the mind and the subject upon which the 
mind acts, but the two terms are often very loosely 
understood. Occasionally we think about this subject 
as something outside of us altogether. For example, 



42 EXPOSITION AND ILLUSTRATION IN TEACHING 

the mind may be said to act upon the colours when we 
watch a sunset. If this be so, the mind is acting upon 
something that is material. But it would be better 
to say that the brain through the medium of the sense 
organs is being affected in a certain way, and that as 
a result the mind is stirred to a particular kind of ac- 
tivity. The fundamental connection between mind 
and matter is fortunately no part of our present busi- 
ness; what we are interested in is the connection be- 
tween the mind and that upon which the mind acts. 
Speaking generally, the mind is said to act upon ideas.^ 
Mental content is usually regarded as being made up of 
ideas. It is a very convenient way of expressing our- 
selves to speak of the mind as a sort of force that acts 
upon certain entities called ideas. But ideas are not 
things from without that the mind takes into itself 
and builds up into useful combinations. Still less are 
they independent entities that act on their own initia- 
tive. Ideas are not so much things as forces. They 
are modes in which the mind manifests its activity. 
It is not so much that the mind has ideas as that the 
mind is ideas. It was formerly fashionable to speak 
of the mind as having a certain number of faculties; 
but recent writers regard the faculties as merely dif- 
ferent ways in which the mind shows its activity: 
they are sometimes spoken of as modes of being con- 
scious.^ This description might be equally applied to 
ideas, the difference being that the ideas are modes 
of consciousness more specialised than are the facul- 

^ Cf. Locke's definition of an idea as "whatsoever is the object of 
the understanding when a man thinks." Human Understanding, 
Bk. I, Chap. 1, §8. 

2 Cf . Professor Stout : Manual of Psychology, Book I, Chap. I. 



MENTAL CONTENT 43 

ties. My idea of a table is my mode of being conscious 
of tables, but it has its peculiarities. My experience 
of tables has not been exactly the same as everybody 
else's, and my mode of being conscious of a table is 
affected accordingly. 

We must not be led into supposing that ideas always 
represent definite separate units such as we call things, 
or even that they always correspond to what are called 
the substantive elements of thought. It is found that 
the elements of thought may be roughly arranged into 
two classes : those upon which the mind may rest for 
at least a brief time, and those that are always on the 
wing and cannot be made by themselves the matter 
of thought, but must always be considered in relation 
to other thought-elements. The first class are called 
the substantive, the second the transitive, elements. 
Naturally these terms are not to be confounded with 
their equivalents in grammar. For the purposes of 
Psychology, for example, a verb may be regarded as a 
substantive. The mind can rest on the idea implied 
in the verb to walk, but it cannot deal with such a word 
as of unless it gets the help of other ideas. The dis- 
tinction between the substantive and transitive must 
not be pushed too far. We can in thought isolate tran- 
sitive ideas and — with the help of other thought-ele- 
ments — deal with them as substantives. Have we 
not erudite notes on such transitive elements as are 
indicated by fjLev and Se ? There is, in fact, always a 
strong tendency to turn the transitive elements into 
substantive. We are disinclined to let an idea act 
merely as a force. We want to pause over it, and wher- 
ever possible, analyse it. In actual experience, how- 
ever, we frequently fail to separate out the definite 



44 EXPOSITION AND ILLUSTRATION IN TEACHING 

meaning of a word (which, of course, represents an idea), 
and yet we can use it quite accurately. We often find 
a difficulty in explaining the meaning of a peculiar turn 
in the mother tongue. We know that the expression is 
correct, and that it is the only expression that will 
meet the case, and yet we cannot explain to the en- 
quiring foreigner why. What is called the Sprachgefiihl 
represents this general sense of the value of certain of the 
transitive elements of thought. ¥/e recognise them as 
forces, though we are not always able to control them. 
The uneasiness we experience in dealing with the tran- 
sitive elements of thought results from a natural ten- 
dency we all have to endow abstractions with a more 
or less independent objective existence. There is, in 
fact, in the human mind a strong bias toward the 
'^ Thing'' stage, and this bias must be allowed for in 
our efforts to convey thoughts from mind to mind. 
The fundamental tendency of the human mind to treat 
thoughts as things is illustrated in the universal bias 
toward personifying the forces of nature. Poets spend 
a good deal of their time in this process of giving to 
airy nothings a local habitation and a name. But 
hypostasis, as this tendency to reify thoughts is called, 
is apt to induce confusion. It leads us to imagine, 
for example, that because we can remember and imag- 
ine and judge we must have faculties of memory, 
imagination, and judgment. A clock can tick, but no 
one thinks of endowing it with the faculty of tickibility. 
Yet if we had occasion to speak a great deal about a 
clock's power of ticking, we would almost certainly fall 
into speaking of its tickibility or its tickipacity. For 
expository purposes it is necessary to have a term to 
describe the various modes of being conscious, and so 



MENTAL CONTENT 45 

long as we do not imagine that there is a thing corre- 
sponding to each of the terms, no harm is done in speak- 
ing of the faculties of memory, imagination, judgment, 
and so forth. 

It is obvious that there is the same tendency to hy- 
postatise the ideas as there is to hypostatise the facul- 
ties. Indeed the two — the ideas and the faculties — 
have so much in common that they must be distin- 
guished, not so much by their fundamental nature as 
by their reference. While both are, as we have seen, 
essentially modes of being conscious, a difference be- 
tween them may be said to be that while all men have 
the same faculties, — though perhaps not of the same 
quality, — all men are far from having the same ideas. 
The fact is that ideas are forces that have brought the. 
mind into touch with something outside itself. They 
therefore either directly, or at one or more removes, 
have a real connection with the outer world. They 
are, in consequence, to some extent dependent upon the 
nature of the environment in which the mind functions. 
The same thing, however, may be said about the facul- 
ties. Memory differs greatly according to the class of 
facts upon which it is exercised. We may all be said 
to have good memories for something. So with imag- 
ination and even reasoning. We always reason more 
easily when dealing with matters v/ith which we are 
familiar. This does not, of course, mean that the reason 
acts in one way in dealing with stocks and shares and 
in another in elaborating metaphysical theories. Simi- 
larly, there are general laws according to which the 
consciousness acts in forming ideas, — laws that are the 
same whether the idea has to do with the concrete or 
the abstract. 



46 EXPOSITION AND ILLUSTRATION IN TEACHING 

A convenient way of expressing the facts of the case 
is to say that some modes of being conscious are more 
general than others, and are called faculties; others 
less general and more affected by what they act on are 
called ideas. Since ideas are so much determined by 
our dealings with the external world, they may be said 
in some sort to represent the external world. This is 
how it comes about that ideas are often spoken of as if 
they were the material upon which the faculties act. 
We do not usually speak of the mind acting upon the 
imagination or the judgment — though, by the way, 
we sometimes hear expressions among those who pro- 
fess to improve the memory that seem to imply an 
action of the mind on the memory — while we do speak 
of its acting upon ideas. It is in this sense that ideas 
may be called the content of the mind, since they pro- 
vide a means by which the activities of the mind may 
be exercised. Memory, judgment, reasoning, and the 
other so-called faculties cannot exist unless they have 
something to exercise themselves upon. They cannot 
carry on their functions in vacuo. They depend upon 
the ideas to provide them with the necessary material 
to operate upon. This may be accepted as a useful 
form of stating the case, but it is necessary to be always 
on our guard against supposing that the ideas are in any 
real sense more material than the mind itself. They 
may be that upon the production and manipulation of 
which the activity of the mind expends itself, but it is 
only in this metaphorical sense that they can be re- 
garded as material. 

While we treat ideas as forces, we are still in danger 
of hypostatisation. They are forces, no doubt, but 
not independent forces. We sometimes speak of them 



MENTAL CONTENT 47 

in a vague way as acting upon the mind. But this is 
always a mistake. They never act upon the mind for 
the reason that they themselves are only modes in 
which the mind acts. It has been suggested that an 
explanation may be effected by regarding the ideas as 
one part of the mind acting upon another part. To 
this no objection need be raised so long as it is clearly 
recognised that the normal healthy mind is after all 
one and indivisible. From its very nature as an or- 
ganism the mind must have action and reaction going 
on within itself, but it must never be forgotten that it 
always remains one organic whole. Ideas are really 
more or less stereotyped modes of being conscious, re- 
sulting from the more or less constant reaction to the 
same sort of conditions. A set of conditions that is 
continually recurring in absolutely the same way 
naturally causes a very definite reaction.^ This gives 
rise to what may be called an idea of great force, say, 
the idea of food. We can think of this idea and speak 
about it without really believing that there is an idea 
of food apart from any mind. When we say that the 
idea of food produces a certain effect on the mind, what 
we really mean is that the mind as a whole is experienc- 
ing a reaction resulting from its own activity in a cer- 
tain direction. When several ideas, say food, hunger, 
poverty, are said to act upon each other, what is meant 
is that the mind is correlating its various activities 
in relation to conditions that lie outside of itself. 



* A skilled mechanic's idea of a hammer is quite different from 
that of, say, a writer of novels. Foremen in works tell us that they 
know the really skilled workman by the way he lifts a hammer. His 
reaction is quite different from that of the casual user of the imple- 
ment. 



48 EXPOSITION AND ILLUSTRATION IN TEACHING 

As a matter of phrasing, therefore, it may be per- 
missible occasionally to speak of ideas as forces acting 
and reacting upon each other. But it has always to 
be kept in view that this is only a mode of expression, 
a convenient figure of speech; and that the mind is the 
sole source of the activity of the ideas. 

From what has been said it follows that ideas are of 
different degrees of remoteness from the outer world. 
Certain ideas can be got directly from without and in 
no other way. The only way to attain to an idea of 
the scent called Eau de Cologne is to experience the 
sensation caused by smelling it. But the idea of scent 
as such is formed within. From without we can get 
such ideas as red, blue, yellow, and green; but we must 
look within for the idea of colour.^ Exposition is quite 
unable to make a congenitally blind person realise what 
blue is, though it may enable him to understand by 
analogy from certain other senses the sort of function 
that colour has in our interpretations of the outer world. 
A blind person may therefore be placed in the position 
of being able to behave quite intelligently in relation 
to certain questions involving colour. 

Since the essential purpose of Exposition is to cause 
to arise in the mind of the pupil a combination of ele- 
ments exactly corresponding to a combination at that 
time existing in the mind of the expositor, it is easy 
to see that in sensory matters, such as colour, taste, and 
smell, it may well happen that Exposition fails because 
the necessary elements are not present in both minds. 

^ For a very graphic and intelligible account of the relation between 
ideas that depend on outward stimulus and those that arise within, 
see Huxley's Hume, p. 68 ff. The whole of the Chapter on The Con- 
tents of the Mind is very illuminating. 



MENTAL CONTENT 49 

But there is a source of danger, even when all the 
elements are present in both minds. It is quite possible 
that the elements may be differently combined in the 
teacher-mind and the pupil-mind. Sometimes the 
combination formed in the pupil's mind is quite reason- 
able, and teacher and pupil may talk for long enough 
about the matter without discovering that they are 
dealing with combinations that do not agree. It was 
only by a chance statement in an examination paper 
that a teacher discovered that one of his best pupils had 
been for years under the impression that John Knox 
had been hanged. The cause of the error was a mis- 
interpretation of the remark made by the teacher in 
class: ^^John Knox was then sent to the galleys. '^ 
Not having heard of the galleys, and being familiar 
with the word gallows, the pupil made the natural 
enough assumption that Knox was hanged. The mis- 
take ought to have been discovered by a comparison 
of dates, but schoolboys are very willing to accept 
on trust a hypothesis that fits in with all the demands 
of a given lesson. Usually the combination of ideas in 
the pupil's mind is, as in this case, quite intelligible 
to the teacher as soon as it is exposed. But occasion- 
ally pupils who have had quite a different early train- 
ing from that of their teachers may make combina- 
tions that are unintelligible even when laid bare. An 
Enghsh Master could not understand the word smake 
that occurred in a Scotch boy's essay. He gathered 
from the context that it was something to eat, but could 
not accept the boy's confident explanation that it was 
a small steak. Careful enquiry brought out the fact 
that in the boy's family circle this was the accepted 
meaning, its origin being a corruption of the metrical 



50 EXPOSITION AND ILLUSTRATION IN TEACHING 

version of the Hundredth Psalm. This had been 
taught to the children before they could read, by mak- 
ing them repeat the words after the nurse. Since they 
could not understand the real sense, they had, from a 
fundamental necessity of human thought, to supply a 
sense of their own. 

Know that the Lord is God indeed ; 

Without our aid he did us make : [did a smake] 

We are his flock, he doth us feed, 

And for his sheep he doth us take. [doth a steak] 

Custom legitimised the new substantive smake in the 
family circle, and the boy did not realise that it was 
not current in the outside world. 

Speaking generally, the best way of preventing serious 
misconceptions of the kind we have been dealing with 
is to encourage the interchange of ideas in class. This 
it is that to some extent justifies the otherwise unrea- 
sonable desire the teacher has for reproduction of knowl- 
edge by the pupil. But the best form of reproduction 
is that which applies knowledge already acquired 
rather than merely produces it for inspection. In the 
give and take of genuine class teaching there is every 
chance that misconceptions of all kinds will be exposed, 
not necessarily to the teacher but to the pupils them- 
selves. Many a brilliant howler is lost to the school 
because the pupil himself learns in time from the work 
that is going on in the class that the answer he would 
have given had he been unfortunate enough to be called 
upon is not exactly the sort of thing that would com- 
mend itself. The teacher has the further satisfaction 
of knowing that not only does this exchange of ideas 
serve the particular ends of Exposition, but is in itself 



MENTAL CONTENT 51 

of such importance that it may fairly be treated as a 
fundamental part of the work of education. Mr. 
H. G. Wells, for example, lays it down that the chief 
function of education is to cultivate just this form of 
interaction: — 

"The pressing business^of the school is to widen the range of inter- 
course. It is only secondarily — so far as schooling goes — or at any 
rate subsequently, that the idea of shaping, or, at least trying to 
shape, the expanded natural man into a citizen comes in." ^ 

It is clear that for this improvement in intercourse 
there must be not only agreement in the methods in 
which minds work, but substantial agreement among 
the results of mental process. To put the matter 
baldly, there must be agreement between the mental 
content of teacher and pupil if there is to be communion 
between them. Exposition has for its aim the estab- 
lishment of this agreement. Even random intercourse 
between teacher and pupil will, if continued long 
enough, lead to the discovery of whatever disagree- 
ments exist between the two mental contents. But 
for satisfactory work it is necessary to have some com- 
mon standard to which both contents may be referred, 
so as to bring out inconsistencies. This standard is 
to be found in the outer world. Teacher and pupil 
alike may test their idea-combinations by comparison 
with what goes on in the world around us. After all, 
our mental content is primarily made up out of our re- 
actions upon the outer world, and the value of our com- 
binations of ideas may be tested by seeing how far they 
will work in relation to the state of things outside of us. 
The combinations in every normal mind can stand this 

* Mankind in the Making, p. 214. 



52 EXPOSITION AND ILLUSTRATION IN TEACHING 

test of seeing whether they ^'work" or not in our or- 
dinary Hfe. Unless our inner world and the outer fit 
into each other, there is obviously something wrong. 
It is not perhaps too strong a statement to make that 
a great deal of exposition has for its object the build- 
ing up in the mind of the pupil of great combinations of 
ideas that correspond with the facts of the outer world. 
It is obviously of the first importance that we should 
carefully consider the nature of the two worlds, and 
particularly their relation to each other. The outer 
world is not only a standard by which to compare two 
inner worlds, — the teacher-world and the pupil-world, 
— but the source of the pattern upon which all inner 
worlds are built. 

The plain man has no difficulty in believing that there 
is a world outside of him, and that this world is full of 
objects upon which he acts and which in turn act upon 
him. He has no doubt whatever that he knows this 
outer world, and that it exists independently of him: 
that it has existed before he was born, and will exist 
when he has passed away. Some people, by reason of 
greater opportunities, may know more of this world 
than do others, but it does not occur to the plain man 
to doubt that it is possible to know it at all. This is 
left for certain philosophers who point out that all we 
can ever know is made up of our own sensations and 
the interactions and combinations of these sensations. 
Out of the elements of sensation each of us builds up a 
world of his own, but thinks that world exists outside. 
At first sight it appears easy to demonstrate the absurd- 
ity of a theory that maintains that there is no outer 
world at all, but that each of us makes up a world of 
his own. So soon as we try, however, we find that the 



MENTAL CONTENT 53 

theory has a great deal of fight in it, and that the 
troublesome philosophers have much to say for them- 
selves. It is found that all our proofs ultimately come 
back to the evidence of our senses. We are confined 
within the circle of our own experience, and though we 
believe that there is an outer world we cannot prove its 
existence. 

Do I see a water carafe before me, or do I only ex- 
perience certain sensations of light and shade ? It 
makes matters no better when I stretch out my hand 
and feel the carafe. I only add a bundle of new sen- 
sations. Even when I pour out some water and drink 
it, I am no further forward. I have only multiplied 
sensations. I have not got beyond the range of my 
own personal experience. I believe that there is a 
carafe there, but I cannot get at it. There is the word 
carafe, and there is the complex bundle of sensations 
that make up my version of a carafe. But is there a real 
carafe, independent of me, — a carafe that exists when 
I am not there to perceive it, a caraf e-in-itself ? This 
problem of the existence of a Thing-in-itself apart from 
any perceiving being is of great importance in philos- 
ophy, but for the plain man it is an excellent problem 
to give up. Let us honestly beg the question. Let 
us acknowledge that we cannot prove the existence of 
an outer world independent of us, and let us at the 
same time take it for granted that there is an outer 
world. 

The very use of the words ''an outer world" implies 
the existence of a world that is not outer. With this 
inner world we are on friendlier terms. We feel at home 
in it. We seem to be free from criticism there. No 
one from without can penetrate within it. We are 



54 EXPOSITION AND ILLUSTRATION IN TEACHING 

ourselves the only persons capable of passing judg- 
ment on its existence and nature. When we speak 
of the mind's eye we imply that there is an inner world 
that we can look upon after the fashion in which we 
examine the outer world. This would suggest a re- 
semblance between the two worlds. Most people when 
questioned would say that their inner world is a repro- 
duction of the outer, a sort of vaguer and less vigorous 
duplicate of what exists outside. As a matter of fact 
the inner world is in part ^ a reproduction of our experi- 
ence of the outer world. When we close our eyes and 
recall a past experience involving elements depending 
on the outer world, there is without doubt a reproduc- 
tion of what occurred in the past including those ele- 
ments; our present vague experience is similar to, 
though feebler than, our past. 

But this is not quite the same thing as to say that the 
inner world resembles the outer. Our mental picture 
of a water carafe, even when we are looking at it,, may 
not at all resemble the real carafe, the carafe-in-itself. 
All that we can say — but this is quite enough for the 
practical purposes of life — is that there is a corre- 
spondence between the inner and the outer worlds: 
they fit into one another, and both remain constant. 
Whatever the carafe-in-itself is really like, it always 
causes the same mental picture to arise when we look 
at it ; it always reacts in the same way to the different 
senses. So that after all what it is really like is not of 
any moment, since we can never by any chance get at 
this real appearance. 

^ Part of our inner world is originated, if the expression may be 
permitted, "on the premises." Our feehngs and desires, for example, 
must be considered as essentially of the inner world alone. 



MENTAL CONTENT 55 

We are apt to picture the inner world as made up of 
ghostly water carafes, tables, houses, mountains, seas, 
skies, clouds, all combined in an orderly way, — a sort of 
well-arranged storehouse of shadowy things that cor- 
respond to the things-in-themselves that form the real 
world. This view may be compared with that stage of 
thought that has been already referred to as the Thing 
stage. In this, the earliest stage of thought, the world 
is assumed to be made up of a great series of indepen- 
dent things, each existing by and for itself. The stage 
is illustrated in the drawings of children and savages. 
There each thing is drawn separately, and set down 
on the paper apart from the others. It is only when 
we begin to see the relations between the individual 
things that we realise that they are not so independent 
of each other as they seem. This marks the rise of the 
Law stage, at which relations are studied and reduced 
to order and classified. Most people pass through 
both the Thing stage and the Law stage. But com- 
paratively few reach the third stage known as System, 
in which the Laws themselves have their meaning 
brought out by being referred to great general prin- 
ciples that dominate them. 

The ^ things '^ that make up the inner world are some- 
times referred to as ideas, concepts, or images. The 
last name is applicable only when we are dealing with 
the direct reproduction of a particular experience. If 
I call up a mental picture of a particular table that I 
am familiar with, I have an image. But if I merely 
think about table in general, I can have no particular 
picture, for I do not know enough about it ; or if you like, 
I know too much. I do not know whether to picture 
the table as round or square, or with four legs or three 



56 EXPOSITION AND ILLUSTRATION IN TEACHING 

or six, and yet I know that it may be pictured in any of 
these ways. This kind of general idea that cannot be 
reduced to a picture is the kind that is properly called 
a concept. It must be general enough to include all 
kinds of things that belong to its class. The concept 
table, for instance, must be ready to include all kinds of 
tables, — round, square, oblong, oval, hexagonal, — 
but it must never he any of these. It has to pay for 
its extreme generality by the loss of the power ever to 
become particular. The concept has the power of 
crystallising out into any particular example of that 
concept, but it possesses this power only on the condi- 
tion that it shall never exercise it, without the result 
ceasing to be a concept and becoming a generalised 
image or type. 

This generalised image or type stands between the 
mere image and the concept. If I look at a particular 
dog Ponto here and now present, I have a percept. 
If in the absence of the dog I call up in my mind a pic- 
ture of this very dog Ponto, I have an image. If now 
I call up in my mind a picture of a dog that is not a re- 
production of any particular dog that I have ever seen, 
but stands for a type of all dogs, a sort of pattern of 
dog in general, I have a generalised image of dog. 
This generalised image differs from the concept, since 
the latter cannot be represented as being any special 
kind of dog at all, but can only be thought about. 
The generalised image of a dog may be any species of 
dog, but it can be of only one species; it may have any 
colour I please (consistent with the possibilities of dog 
nature), but it must have some colour; and so on. The 
conceptual dog has all the qualities that are essential 
to all dogs : it must have four legs, a tail, two eyes, hair. 



MENTAL CONTENT 57 

and so forth ; it must have colour, but no special colour; 
must have size and weight, but no fixed size and weight. 
Thus the concept gains in generality what it loses in 
definiteness. 

Even in reading about the concept one gets irritated 
at its extreme elusiveness, and in actual experience 
people fall back in despair upon the generalised image 
and do their thinking by means of that. We shall 
see later that some writers object very much to this 
more or less pictorial thinking, and certainly it has some 
disadvantages. We must not give up the freedom 
of thought that comes from the extreme generality 
of the concept, but on the other hand we need the sup- 
port of the generalised image to assist the mind in 
dealing with concepts. When we use the generalised 
image, we are really thinking of ^^dog in general, '^ 
but by means of a concrete particular dog — though 
which particular dog is irrelevant. 

The question may now be asked whether the inner 
world is made up of concepts or images. It would 
appear that there is room for nothing but images. 
How can one construct a world in which tables are not 
allowed to be any particular kind of tables, but only 
tables in general, that can be thought about but not 
represented ? This difficulty brings out the distinction 
between the static and the dynamic view of the concept. 
Each of the views is sound though each emphasises 
a different aspect. 

The static view of the inner world is that it is made 
up of a great mass of more or less attenuated represen- 
tations of ^'things," all arranged so as to fit into each 
other^s qualities and positions. But such a world is 
inert, dead. It exists only to be examined by logical 



58 EXPOSITION AND ILLUSTRATION IN TEACHING 

persons who are concerned about definition and classi- 
fication. For the ordinary needs of hfe there must be 
the possibiUty of interaction among the elements that 
make up the inner world. It is here that the dynamic 
view has the advantage. The concept of a table is no 
longer to be treated as a mere group of the essential 
qualities of a table, but as a force determining particu- 
lar lines of action. If you ask an ordinary intelligent 
person what a table is, you will probably find that he 
has some little difficulty in saying precisely. Does 
this mean that because he cannot define a table he does 
not know what a table is ? Assuredly not. He is able 
to behave intelligently in relation to tables. To under- 
stand a term it is not necessary that one should be able 
to define it. 

Definition has no doubt its proper place. The 
moment we need to discriminate carefully between 
different terms, we have to define them more or less 
accurately, and more or less consciously. But we must 
not let the definition dominate us. If we are asked: 
what is chalk ? we may turn to the dictionary and find 
that it is "a soft earthy substance of a white, grayish, 
or yellowish white colour, ^^ etc., or we may simply say: 
it is something to write on a blackboard with, or to im- 
prove the head of a billiard cue with, or to make car- 
bonic acid out of. Some are inclined to say that these 
are purposes to which chalk can be applied, but that 
they do not tell us what it is. Chalk, they say, is a 
chemical compound represented by the formula CaCOs, 
that and nothing else. But chalk is as much a thing to 
write with as it is a chemical compound. This is a 
world in which we react upon chalk in various ways, 
one of them being a chemical way; but this way is no 



MENTAL CONTENT 59 

more fundamental than the others. We must remember 
that classification is of the mind and not of the world. 
We find it necessary for our human needs to classify 
objects, but this is for our convenience, and is not at 
all binding upon nature. Among young students there 
is sometimes a certain impatience with Nature. They 
get their carefully prepared classification in books, and 
are not a little indignant with Nature when she does 
not see her way to fit into the arrangement in every 
case. For example, there is a troublesome little Aus- 
tralian mammal, called the ornithorhynchus anatinus, 
that is the despair of the taxonomist. It is a web- 
footed quadruped, with a bill like a duck ; and it lays 
eggs like a bird or reptile. There is no place for this 
creature in any of the recognised classes, and to make 
a new class for it by itself is extremely disconcerting. 
There is a touch of remonstrance even in the state- 
ment of the sober taxonomist : — 

"The lowest order of the Mammalia is that of the Monotremata, 
constituting by itself the division, Ornithodelphia, and containing 
only two genera, both belonging to Australia — namely, the Ornitho- 
rhynchus and the Echidna. '^ ^ 

This is not the place to show the value of such a 
hybrid specimen in leading us to discover the real 
nature of the different classes to which it might claim 
doubtful admission, and especially in making clear the 
relation between these classes. What is more germane 
to our subject is the question of what place is to be 
found in the mental content for such exceptional cases. 
Ruled out of the well-known bird and reptile classes 
and thrust into a little class of its own, the ornitho- 
rhynchus is still intelHgible to us ; we at least know what 

^ H. A. Nicholson : Manual of Zoology, p. 630. 



60 EXPOSITION AND ILLUSTRATION IN TEACHING 

we mean in speaking of it. Everyone who has read this 
chapter thus far has formed some sort of idea of the 
creature, and there are as many ideas of the ornitho- 
rhynchus as there are people who use the term. If the 
reader examines his idea, he will find that it is modified 
by what he knows about Australia, about ducks, about 
bills, about mammals, quadrupeds, eggs, birds, reptiles, 
and even Greek. 

In spite of all such troublesome exceptions there is a 
use for the exact classification that admits of no devia- 
tion from the strict marks that distinguish each group. 
Classification is of the mind, and so is the idea of the 
unclassifiable ornithorhynchus. But each represents 
a different department of mental activity. The limita- 
tions imposed by the laws of classification are logical; 
the additional materials supplied from individual ex- 
perience of exceptions to those laws have to be dealt 
with as psychological units. 

In the next chapter ideas will be treated as active. 
Here it will be enough to deal with them as the elements 
out of which certain combinations are to be formed. 
In Exposition the teacher has already in his mind a 
certain more or less elaborate combination of ideas, 
forming the expositandum. The pupil may have all 
the necessary ideas lying about loose, as it were. It is, 
then, the teacher's business to build up those ideas 
in the pupil's mind into the desired whole. It may be 
(in fact, this is the ordinary case) that the pupil has only 
certain of the needful ideas at his disposal. In this 
case the teacher has to present the necessary nev/ ideas 
as well as to arrange the ideas at present possessed by 
the pupil. 

Exposition may therefore be regarded as essentially 



MENTAL CONTENT 61 

a constructive process, and under ideal conditions it 
need never be destructive. In building up knowledge, 
fact should be added to fact in such a way that it is 
never necessary to undo what has been done. A com- 
bination of ideas once formed should be for all time. 
Something approaching this ideal state of affairs may 
be reached in the case of subjects that are removed from 
the ordinary interests of everyday life. In certain 
branches of Mathematics, and in the higher reaches of 
many of the other school subjects, it is possible for the 
teacher so to dominate the presentation of entirely 
fresh matter that each new fact falls exactly into its 
appropriate place. In teaching Latin, for example, 
there is nothing to prevent the master from deliberately 
determining beforehand the exact order in which the 
various points shall be presented to the pupil. Yet 
even when, as in this case, the arrangement of the pres- 
entation is entirely in the hands of the teacher, it some- 
times occurs that in order to give complete understand- 
ing of a given fact two other facts must be presented 
simultaneously. Neither without the other will be 
capable of throwing light upon the point to be explained, 
and since in actual practice one must precede the other, 
it is occasionally necessary to present one because, on 
the whole, it is somewhat more relevant than the other, 
and yet the fact that has lost precedence may in cer- 
tain respects deserve to come first. 

Apart from this difficulty that is inherent in the na- 
ture of things, there is the ever present trouble that we 
can in almost no case start quite fair. We have very 
seldom indeed the clean sheet that ideal exposition 
demands. Our pupils generally come to us with their 
mental content already fixed with regard to many of 



62 EXPOSITION AND ILLUSTRATION IN TEACHING 

the matters we have to deal with. Accordingly we 
cannot limit ourselves to the building up of new wholes 
out of entirely fresh elements. Our elements are not 
fresh, and there are wholes already in existence. 

Thus it comes about that there is a destructive as 
well as a constructive stage in Exposition. When the 
existing combination of ideas is not to our satisfaction, 
we must demolish it before we can begin to reconstruct 
it in the way we desire. We are all familiar with what 
takes place when a pupil changes from one teacher of 
the violin to another. Almost invariably the master 
is determined to have his style of execution adopted, 
and in order to secure this insists upon his pupil begin- 
ning again at the very beginning. When the violinist 
turns back his pupil in this way, his idea is to break up 
the previously formed coordination of muscular actions, 
and establish in its place a coordination that will fit 
in with the later complex movements demanded by 
the approved execution. In ordinary exposition it is 
seldom that we require to carry destructive work so far. 
It is usually unnecessary to reduce a given combination 
to its elements in order to correct some false colloca- 
tion. The pupil may have the view that the further 
south one goes the warmer it becomes. All his ex- 
perience warrants him in maintaining this view, and 
he holds it with some vigour. It is not at all necessary 
that the complex that corresponds to ^^ south" in his 
mind should be reduced to its elements and painfully 
reconstructed on correct lines. All that is necessary 
is to break up the existing unwarrantable connection 
between south and increasing temperature. To the 
pupil south still remains south in every other attribute, 
but the new element of relativity is introduced, and the 



MENTAL CONTENT 63 

pupil learns that while moving to the south always in- 
volves change of average temperature, it does not al- 
ways involve the same kind of change. In ordinary 
exposition it is usually sufficient to stop far short of 
ultimate analysis, and to begin the reconstructive pro- 
cess with units that are not nearly the lowest possible. 

Further, it has to be noted that the destructive pro- 
cess may be necessary, not because the combination is in 
itself objectionable, but because there is a need for the 
elements of which it is composed, in order to build up 
a new complex. In a given combination certain ele- 
ments become so firmly welded together that their 
individual existence is overlooked, and it becomes the 
teacher's business to break up the fixed combination 
so that the elements may become available in other 
connections. 

In the ultimate resort, however. Exposition as Ex- 
position is a process of building up. The destructive 
process is no doubt important, and indeed essential, 
but it is none the less merely preparatory to the real 
work of Exposition which is constructive. Learning 
a subject means really the building up of various ideas 
into an organised whole in which each finds its appro- 
priate place. Ideas in this sense must be regarded as 
representing activities. It is only when fact has be- 
come faculty that we have really learned. 

It is clear that when we speak of a combination of 
mental elements, we give no indication of the extent to 
which the combination is carried. In Exposition we 
have frequently to seek out simpler ideas in order to 
explain those that are more complex. The unit of 
Exposition therefore becomes important. Naturally 
the ultimate unit is the individual idea. But in 



64 EXPOSITION AND ILLUSTRATION IN TEACHING 

practice the simple individual idea is found to be very 
difficult to separate out and manipulate. It has always 
a strong tendency to take to itself other elements and 
appear as a complex. In what are called ^'Object 
Lessons'' in school there is a strong tendency on the 
part of the teacher to wander into an explanation of the 
qualities of objects, and to lose sight of the object itself. 
The teacher yields to the lust of analysis. Whatever 
the subject, the lesson is apt to drift into a discussion 
of the meaning of such terms as opaque, brittle, elastic, 
fluid, friable, metallic. But while the teacher's ten- 
denc3^ is thus towards abstraction, the pupils are in- 
clined the other way, and are found to be continually 
interpreting the abstract terms in connection with con- 
crete objects. When the teacher wishes to elicit the 
idea of whiteness, he gets from the pupil the answer 
chalk. ^^What do you mean by brittle?" asks the 
teacher, and the natural answer is glass. 

The unit of exposition must naturally vary with the 
stage of advancement of the pupil. As we progress in a 
subject the unit naturally grows bigger. Very many 
errors in exposition arise from using a bigger unit than 
the state of advancement of the pupils warrants. 



CHAPTER III 

Mental Activity 

The Laws of Thought as Thought are purely general 
and abstract. They take no account of the material 
upon which the mind acts. Yet this material is of the 
very essence of Exposition. We have seen that under 
certain reservations we may regard ideas as the material 
upon which the mind operates. This is their passive 
aspect. Ideas in this relation are regarded as the mere 
furniture of the mind, its stock in trade, its acquired 
possessions. So treated they are termed '^ presented 
content.'^ 

Ideas are also said to possess a certain degree of 
'Tresentative activity,'^ which may be generally de- 
fined as the power to force an admission into conscious- 
ness. Every idea that has ever been in consciousness 
has by that very fact acquired a certain degree of this 
activity, and this amount is increased every time the 
idea finds its way back into consciousness. It is con- 
ceivable that at a given moment the presentative ac- 
tivity of every idea that has ever passed through a given 
mind should be tested and registered. If this practically 
impossible feat could be accomplished, we would have a 
systematic arrangement of ideas in order of their accu- 
mulated presentative activity for that mind. Now it 
is clear that if this state of affairs represented the whole 
truth, only a few ideas would ever get into the mind at 

F 65 



66 EXPOSITION AND ILLUSTRATION IN TEACHING 

all, unless it were able to take in an unlimited number 
of ideas at a time. For naturally those with the great- 
est presentative activity would force their way into the 
mind and would resist all the attempts of the less power- 
ful ideas to dislodge them. As a matter of fact, how- 
ever, ideas with comparatively little accumulated pre- 
sentative activity may acquire a temporary power 
sufficient to dislodge for the moment all others. Sup- 
pose we are studying Shakespeare. The ideas called 
up by his plays have in the course of time acquired a 
great accumulation of presentative activity. Yet at 
the moment of our most intense study of As You Like 
It a sudden street call may displace Rosalind and 
Orlando from our thoughts in favour of shrimps or cat's 
meat. To be sure the Shakespearian ideas immediately 
resume their place in virtue of their greater accumu- 
lated activity as individual ideas, and also because of 
the support they give to one another as parts of an 
organised group. 

For ideas do not remain in the consciousness as iso- 
lated units. They are always bound more or less 
closely to the other ideas that happen to be present in 
the consciousness with them. It is, of course, impossible 
to say how many ideas may be in the consciousness at 
any one time. The number must vary greatly accord- 
ing to the degree of concentration that marks the 
moment. It may be said that if there are one or two 
particularly active ideas in the mind, there is no room 
for any others. The same fact may be more truly ex- 
pressed by saying that the consciousness is sometimes 
concentrated on a few points and sometimes spread over 
a large number. Except in pathological cases there 
are always more than one idea present in the conscious- 



MENTAL ACTIVITY 67 

ness, and in normal cases there is usually a more or less 
uniform distribution of the available consciousness 
among the ideas presented. It is common to speak of 
the ^ Afield of consciousness '^ as representing the area 
within which ideas are active. This field is often re- 
garded as being round, perhaps from a more or less con- 
scious comparison with the field of vision as dealt with 
in linear perspective, where it is represented by the base 
of the cone of visual rays. Within this field some of the 
ideas appeal to us at a given moment much more than 
do others. We figure those ideas to ourselves as oc- 
cupying the centre of the field, and therefore we call 
them focal. Those somewhat removed from the centre 
may be called subfocal, those near the circumference 
submarginal, and those on the circumference marginal. 
The nearer an idea is to the centre, the greater its share 
of consciousness. It is obvious that the same fact may 
be expressed by saying that the ideas with the strongest 
presentative activity occupy the centre, and those of 
less activity have to content themselves with a place in 
the subfocal, submarginal, or marginal area. In other 
words we may speak literally of the distribution of con- 
sciousness, or metaphorically of the activity of the ideas. 
In order to make this figure workable it is probably 
necessary to assume that the field of consciousness is 
capable of more or less rapid change of area. Some- 
times it is very small and contains onh^ a few ideas. 
Under such circumstances the distinction between focal 
and marginal almost disappears; the few ideas present 
are practically all focal. At other times the area is 
wide, and the number of ideas correspondingly in- 
creased. Here the focal ideas are not so intense, as 
in the case of the smaller field, but they are much more 



68 EXPOSITION AND ILLUSTRATION IN TEACHING 

intense than are those in the outlying regions. We have 
to assume that the total amount of consciousness avail- 
able at a given moment is limited, and that therefore 
the problem is largely one of distribution. 

There is danger of overrigidity in the figure. No 
exact line of demarcation can be drawn between focal 
and subfocal near the centre, and none between mar- 
ginal and submarginal near the circumference. The 
figure of the field has the advantage that it renders 
impossible the older view that really implied that only 
one idea at a time passed through the consciousness. 
In psychology it is frequently necessary to correct one 
metaphor by means of another. The 'Afield of con- 
sciousness" figure corrects the old linear view that con- 
fined itself to the seriatim procession of the focal ideas, 
but in its turn errs by confining itself to one plane. 
Professor James's ^ figure of the ^^ stream of conscious- 
ness" or the ^'stream of thought" with his various 
graphic illustrations emphasises the element of bulk or 
mass in our mental content. It has the further advan- 
tage of indicating a procession of force as well as mate- 
rial. In the field figure there is merely the suggestion of 
a place where the ideas may disport themselves. The 
stream figure, by its very nature, implies the crowding 
in of new matter and the passing away of old. Nat- 
urally the figure must not be too closely pressed, for 
in thought there is usually a core of preferred ideas that 
retain their place in the middle of the stream, while 
a great body of ideas pass rapidly along at the margins ; 
whereas in a real river the opposite is the case, for the 
water in the middle moves more rapidly than the water 
at the margins. 

* Principles of Psychology, Vol. I, p. 279 ff. 



MENTAL ACTIVITY 69 

It will probably be well now to pass on to a more 
general statement of the case in less figurative terms. 
The word continuum is becoming more and more pop- 
ular as a term to describe the mental content at any 
given moment. The word indicates a great mass of 
ideas held before the mind; but the ideas are not re- 
garded as lying loose, they are bound to one another, 
they form a more or less homogeneous whole. The 
binding force may be said to be a common purpose or 
a common interest. The purposive interest that dom- 
inates the continuum may be concentrated, and may 
tend therefore to limit the number of elements; or 
it may be diffused, and may take in a large number of 
elements. But whether the elements of a continuum 
are few or many, they never remain long fixed in the 
same relation to one another. Constant change is of 
the essence of the continuum. There is a continuous 
coming and going of mental elements. When we are 
thinking steadily on a given subject, the core of the 
continuum will be fairly large in proportion to the 
whole, and will remain fairly constant ; whereas in easy 
general talk, or in attending to the details of ordinary 
life, the continuum is liable to violent changes in its 
elements, and the core is restricted to that minimum 
of common elements that ensures the preservation of 
our sense of identity. 

We have treated the elements that form a continuum 
as if they were separate from each other. No doubt 
in ultimate analysis the contents of any continuum 
could thus be reduced to independent elemental units; 
but in practice it is found that ideas have a tendency 
to group themselves. Under identical circumstances 
in the experience of the same individual certain con- 



70 EXPOSITION AND ILLUSTRATION IN TEACHING 

tinuums are likely to have almost identical content. 
But even in a continuum that has never before invaded 
consciousness it will be found that its elements are more 
or less definitely arranged in groups. These groups of 
ideas, sometimes known as apperception masses, have 
been formed by the co-presentation in consciousness 
of the ideas in question. They must therefore have 
formed part of previous continuums, though their ac- 
companiments in any two of these continuums may 
never have been the same. In considering how these 
groups have been formed it will be well in the first place 
to begin from the side of the mind rather than from 
that of the idea, in order to counteract the tendency to 
regard the ideas as things independent of the mind. 
After the mental activity has been acknowledged there 
will be less harm in working out the attractive mechan- 
ism of apperception in terms of ideas. 

In the older fashioned theories of the Association of 
Ideas certain general principles were laid down that 
were useful enough so far as they went. But even 
when they were gathered up into one generalisation, as 
in Sir William Hamilton's Redintegration,^ they gave 
little help in the way of explaining the building up of 
great groups of ideas, though they certainly explained 
very ingeniously many mental phenomena after they 
had occurred. Fr. Paulhan, in his UActivite Mentale, 
works out a more active system of association which 
ultimately resolves itself into two great laws — a posi- 
tive and a negative. The positive law he calls the law 
of systematic association. It runs: — 

" Every psychical fact tends to associate to itself, and cause to 
develop, the psychical facts which may harmonise with it, which 

* Lectures on Metaj^hysics, Lecture XXXII, p. 238. 



MENTAL ACTIVITY 71 

may strive with it towards a common goal or for complementary 
ends, which, along with it, may be able to form a system." ^ 

The negative law deals with inhibition or arrest : — 

" Every psychical phenomenon tends to prevent the production 
or development, or to cause the disappearance, of psychical phe- 
nomena which cannot be united to itself according to the law of sys- 
tematic association ; that is to say, which cannot be united with it 
for a common end." ^ 

These two laws, working under the impulse of purpose, 
secure that the various modes of being conscious that 
are of special value to the mind shall recur with suffi- 
cient frequency to establish an ease in reinstating them- 
selves whenever they are called for, and we have thus 
the beginning of the activity that results in the organi- 
sation of the mental processes in relation to the mental 
content. What we call organised groups of ideas or 
apperception masses may, from another point of view, 
be regarded as organised modes of being conscious. 

Treating the matter now from the point of view of 
the ideas, it is to be noticed that the two most important 
laws correspond in general with those of Paulhan. 
Ideas that are called contrary ideas, that is, ideas that 
belong to the same category but differ within that cate- 
gory (such as blue, green, and yellow, which come under 
the same category of colour, but differ inasmuch as they 
are different colours), arrest one another. This means 
that in the competition to enter consciousness contrary 
ideas oppose each other, do everything they can to eject 
each other, and finally as the result of the strife one or 
other succeeds in effecting an entrance and in expelling 
the other. It may be objected that two contrary ideas 
may occupy the consciousness at the same time. We 

^ L'AcHvite Mentale, p. 88. 2 75^^?^ p_ 22I. 



72 EXPOSITION AND ILLUSTRATION IN TEACHING 

amy think of a geranium with green leaves and red 
petals. But here the ideas of red and green are not 
treated by the mind as mere colours, but only as aspects 
of a whole. We think of a geranium in fact, not of red 
and green. This brings out the distinction between 
the having of an idea and the realising of that idea. 
When we merely have an idea, or admit an idea to the 
mind, we treat it as a more or less representative ele- 
ment that embodies a meaning or is significant of 
something else. To realise the idea of red we must 
concentrate upon it all the forces that are appropriate 
to an idea of colour, and in so doing we are drawing off 
all the force that might otherwise have been concen- 
trated upon green or some other colour. In so far then 
as red and green as colours both retain their place in 
consciousness, neither is fully realised, and their 
relation to each other, and to the mind in which they 
are found, is one of unstable equilibrium, the force 
of each being spent in trying to further its own fuller 
development, and to eject the other from conscious- 
ness. 

The law of systematic association, on the other hand, 
applies to those ideas that are known as disparate. 
These ideas have no inherent relation to each other; 
they do not belong to the same category, and so can be 
formed into any sort of complexes that circumstances 
may favour. There is no inherent connection, so far as 
we know, between a grey overcoat, a white horse, and 
Napoleon I,^ yet by the actual collocation of these ideas 
in history they form a complex that has a certain sta- 
bility of its own. Taking that overworked example 

^ If we could view these elements sub specie cEternitatis, no doubt 
we could discover a sufficient cause for their collocation. 



MENTAL ACTIVITY 73 

of the psychologists, the orange, we find that its quali- 
ties are grouped together in the same way. All the 
ordinary complexes of life are built up in accordance 
with the law of systematic association, or the law 
of complication, as it may be called, when regarded 
from the point of view of the ideas rather than of the 
mind. 

Besides the two forces of complication and arrest 
there is a third that has to be taken into account in 
connection with the interaction of ideas. This is 
known as fusion. When an idea recurs in the mind 
it fuses with the traces it left at its previous visit. 
It is by this force of fusion that our elementary ideas 
acquire the stability that is so necessary as a founda- 
tion for the whole superstructure of ideas. In the 
case of two complexes being brought into conscious- 
ness together, all the similar elements in the two fuse, 
all the disparate elements proceed to form a new and 
more elaborate complex, while the contrary ideas 
arrest each other. It must not be supposed that 
fusion is limited to the substantive elements of thought. 
Similar relations that recur fuse as to their common 
elements, and strengthen the idea of their particular 
class of relation. The compelling power of analogy 
owes much to fusion. 

Fusion is always at work in the mind. For the com- 
mon elements in the different groups strengthen each 
other as elements, every time they appear in conscious- 
ness. Two ideas that are contrary to each other, and 
therefore seek to arrest each other, still so react upon 
the rest of the mental content that by fusing with sim- 
ilar elements in that content they really acquire each 
a little more strength; that is, increase their accumu- 



74 EXPOSITION AND ILLUSTRATION IN TEACHING 

lated presentative activity, even while being driven out 
of consciousness for the moment by a stronger rival. 

Complication is obviously the converse of analysis. 
After we have broken up one group of ideas in order to 
reconstruct the elements into another, the rebuilding 
is largely a matter of complication. Naturally fusion 
is going on parallel with complication; for all the ele- 
ments common to the two groups, instead of forming a 
complex, merely go to strengthen each other. But 
arrest is also present in complication. Its main work 
in forming new groups is to prevent the accumulation 
of unnecessary details. 

Every idea seeks to introduce into consciousness all 
the other ideas with which it has formed connections. 
An idea therefore that forms a part of many apper- 
ception masses has a dangerous tendency to recall too 
many ideas with which it is allied in different groups. 
Of the ideas thus invited into the consciousness some 
set up a process of fusion, and others of complication, 
but a large number are cut off by the process of arrest. 
If it were not so, thinking would become impossible. 
The mind would be smothered under the crowd of 
ideas. 

Exposition consists fundamentally of the establish- 
ment of new combinations of ideas, or of the making 
clear and strong combinations that at present exist in a 
vague and feeble way. To give the new combinations 
strength we must have as great an amount of fusion as 
is possible under the circumstances. Richness and 
breadth depend upon complication. Clearness and 
definiteness are gained by arrest. That all three pro- 
cesses may produce their best results there must be many 
presentations of ideas and idea groups. But this is 



MENTAL ACTIVITY 75 

largely the work of Illustration, and will be dealt with 
in later chapters. 

In addition to the Laws of Thought as Thought and 
the various laws of association with which we have 
dealt, there is another law of greater generality and of 
fundamental importance in the art of Exposition. 
It is, in fact, the ultimate impulse to mental activity, 
the equivalent in the mind to gravitation in the mate- 
rial world. It may be called the Law of Mental Har- 
mony. The ideas within the mind must be at peace 
with each other. The moment friction arises there 
must be ceaseless activity till the disagreement is 
removed. Consistency among the ideas is an essential 
to mind. All the mental content must be harmonised; 
there must be no contradiction in the arrangement 
that has been imposed upon the ideas. It does not, of 
course, follow that each mind must be able to resolve 
all the contradictions that occur in the course of 
thought, but the mind must try to reconcile them. 
This is of its very nature, and the necessity is not 
limited to the intellectual class. The mind of the sav- 
age is as sensitive to the need for internal peace as is 
the mind of the savant. On the other hand, the uni- 
versality of the need for internal peace is compensated 
for by the varying degrees of reconciliations that will 
satisfy it. What the savage cannot explain in terms 
of science he can in terms of superstition. In fact one 
of the main functions of superstition would seem to be 
the satisfaction of this imperious mental need. The 
invisible wind has no mouth to make the weird moan- 
ings that disturb him, so the savage is impelled to get 
rid of this apparent contradiction of the rest of . his ex- 
perience. Accordingly he personifies the wind and 



76 EXPOSITION AND ILLUSTRATION IN TEACHING 

thus supplies it with the necessary apparatus, without 
rousing any further difficulty. At later stages, it is 
true, the latent difficulties appear, and the more 
sophisticated successor of the savage has to invent 
some other plausible explanation. The mind is exact- 
ing in its demand for some explanation or other; 
it is less exacting in the quality of the explanation it 
accepts. 

Herbert Spencer gives an interesting account of the 
stages by which he arrived at what he considered to be 
the truth ^ about the colour of shadows. At the first 
stage he regarded them as black, since he had been ac- 
customed to use India ink to represent them in his 
drawings. At eighteen he was told by a friend that all 
shadows are neutral tint, but ^4t was only after my 
friend had repeatedly drawn my attention to instances 
in nature, that I finally gave in.^' He held the neutral- 
tint view for some years, though he did observe 'Hhat 
the tone of the neutral tint varied considerably in dif- 
ferent shadows.'' The divergences, however, ^^were 
not such as to shake my faith in the dogma." His 
peace of mind was at last disturbed by a statement in 
a popular work on Optics: ^Hhe colour of a shadow is 
always the complement of the colour of the light casting 
it.'' He wanted to know " Why are shadows coloured? 
and what determines the colour?" As a result of his 
investigations : — 

"It became manifest that as a space in shadow is a space from 
which the direct Hght alone is excluded, and into which the indirect 
light (namely, that reflected from surrounding objects by the clouds 
and sky) continues to fall, the colour of a shadow must partake of the 
colour of everything that can either radiate or reflect light into it. 

» "The Valuation of Evidence," Essmjs (1891), Vol. II, p. 161. 



MENTAL ACTIVITY 77 

Hence the colour of a shadow must be the average colour of the diffused 
light; and must vary, as that varies, with the colours of all surround- 
ing things. Thus was at once explained the inconstancy I had al- 
ready noticed ; and I presently recognised in Nature that which the 
theory implies — namely, that a shadow may have any colour 
whatever, according to circumstances. 

" Here, then, respecting certain simple phenomena that are hourly 
visible, are three successive convictions ; each of them based on years 
of observation ; each of them held with unhesitating confidence ; 
and yet only one — as I now beheve — true." 

Further, the mind does not go out of its way to seek 
for troublesome inconsistencies. So long as no ques- 
tions are raised it is quite content to accept things as 
they are. A teacher, giving a lesson to a young class 
on a bluebottle, asked how the creature made its famil- 
iar buzzing noise. When she received an answer, she 
told the children that she expected that answer. Of 
course they thought the bluebottle buzzed with its 
mouth because when they wanted to buzz they did it 
with their mouths. Accepting the teacher's word that 
they were wrong, the class had no peace till she told 
them that the buzzing was caused by the wings. This 
gave the children perfect satisfaction, as it did the 
teacher, till her Normal Master pointed out that if 
you remove the bluebottle's wings, it does not stop 
buzzing, but actually buzzes a little harder than usual. 
It was now the teacher's turn to be worried, and it was 
not till she had learned about the special little buzzing 
organ * that she could drop the subject and be at peace 
once more. 

Every mind contains a large number of contradic- 
tions that give rise to no trouble because they are not 

^Discovered by Landois. T. H. Huxley: Anatomy of Inverte- 
brated Animals, p. 377. 



78 EXPOSITION AND ILLUSTRATION IN TEACHING 

perceived. The two sets of facts lie apart, and are 
never brought into contact with each other, so the mind 
is content with its erroneous correlation. It was an 
experienced M.D. with a tincture of literature who con- 
fessed that he had just discovered the true meaning of 
a ^' flash in the pan.^' He had all along associated the 
proverb with the frying pan. He knew quite as much 
about flintlocks as about frying pans, but he had never 
had occasion to connect the proverb with the firearm. 
The same sort of thing is seen in relation to our precepts 
of religion and of business. We usually keep them 
carefully apart. Indeed it is the business of the earnest 
and faithful clergyman to bring face to face the pre- 
cepts from the two spheres and ask his congregation to 
reconcile them. His success is measured by the degree 
of discomfort he is able to introduce into the minds of 
his hearers. So soon as he has introduced dispeace 
among the elements of the mental content he has pro- 
duced a disturbance that cannot be set at rest till in 
some way or other the exposed contradiction is recon- 
ciled. No doubt churchgoers are often very successful 
in effecting a superficial reconciliation, but this must be 
honestly satisfactory so far as it goes, if the person 
affected is to get any peace. 

There is no such thing as deliberate self-deception in 
our attempts to restore harmony between apparent 
contradictions. The wish no doubt is often father to 
the thought, but in the cases we have in view the con- 
tradiction is assumed to have been brought to light and 
placed clearly before the consciousness, so that the wish 
cannot generate the thought, much as the mind may 
desire it. When Shakespeare says of the false Duke 
Antonio, — 



MENTAL ACTIVITY 79 

"Who having unto truth, by telling of it, 
Made such a sinner of his memory, 
To credit his own lie, — he did believe 
He was indeed the duke,"^ 

he is describing what Antonio would have liked to 
believe, rather than what he did believe. No doubt 
the usurper was full of arguments to justify himself 
in ousting his brother, and these arguments probably 
gave him a great deal of consolation, but they could 
never convince him that ^'he was indeed the duke.*' 
As a matter of fact the greater the efforts he made to 
deceive himself, the less likely would he be to attain 
his end, for he would only be keeping more prominently 
before consciousness the contradiction that he wished 
to remove. In his efforts to deceive himself he would 
be doing what the good expositor is continually doing 
when he seeks to break up a false combination of ideas 
in order to substitute a true one. For this co-presen- 
tation in consciousness of ideas that are really con- 
tradictory to each other is an essential part of the 
process of Exposition. It may be called Confrontation^ 
since it implies the bringing face to face of ideas that 
cannot live peaceably together. 

In Confrontation it is assumed that both terms of 
the contradiction are known to the person concerned. 
If this is not the case, no real confrontation can take 
place. I once tried to prove to an Arran farmer that 
the earth is round. I did not succeed. He was in the 
wrong, no doubt, but his was a mind of the most vigor- 
ous kind, a mind that worked admirably within its 
limits. These limits excluded all the scientific ideas 
that make it necessary to believe that the earth is 

» The Tempest, Act I, Sc. 2. 



80 EXPOSITION AND ILLUSTRATION IN TEACHING 

round. All the ideas that had access to the farmer's 
mind were on the most friendly terms with all the other 
ideas to be found there. So soon as anyone is able to 
introduce into that man's -mind an idea that is incon- 
sistent with the flatness of the earth, a disturbance will 
be set up that may lead to the true arrangement of his 
ideas on this subject, but is more likely to lead to a rear- 
rangement which shall explain the particular inconsis- 
tency of which he has been made conscious, without 
necessarily corresponding with what we call fact. 

The principle of Confrontation is nowhere better 
illustrated than in the Socratic method. It was the 
custom of Socrates to begin his discussions by a demand 
for a definition, which in his ironical way he often rep- 
resented to be a help to himself in getting at the true 
meaning of the subject under discussion. It was not 
long before he proceeded to confront the ideas put for- 
ward by his interlocutor with certain other ideas that 
he knew formed a part of that interlocutor's mental 
content. The opposition thus disclosed gave an excel- 
lent opportunity of stimulating that enquiry that was 
always Socrates' aim. The method, in fact, has almost 
always three stages. First there is confidence without 
proper foundation; next as the result of Confrontation 
there arises doubt and desire to attain to the truth; 
then in the third place comes certainty founded on 
legitimate grounds. It is true that in some of the 
actual Socratic dialogues the third stage is not attained, 
the master contenting himself with the disturbance 
that he had set up, well knowing that the interlocutors 
could not settle down till they had reached some sort 
of conclusion, which if not perhaps so satisfactory 
as one that could have been supplied, had at any 



MENTAL ACTIVITY 81 

rate the compensating advantage of having been at- 
tained by the effort of the thinker himself. This 
method of unfinished exposition may be permissible in 
the case of advanced pupils, but with the ordinary 
schoolboy it is generally better to carry the dialogue 
to its legitimate conclusion. The work of the ordinary 
school affords many opportunities to apply the method 
of Confrontation. 

To illustrate, take the case of that constant diffi- 
culty at the early stages of composition, the incomplete 
sentence. Pupils brought up in illiterate homes are 
very apt to make a relative clause stand by itself, 
with no other help than the original grammatical sub- 
ject. In schools where the pupils come from homes 
in which grammatical English is habitually spoken, there 
is not so much danger of this particular form of error, 
but every teacher in a school for the poorer classes is 
unpleasantly familiar with such a sentence in a pupil's 
exercise book as — 

John who broke the window 

The following is a verbatim reproduction of a lesson 
actually given to a class of about sixty-five rather dull 
boys of average age 11 J. The sentence had occurred 
in one of the class exercise books, and was placed on the 
blackboard, as it had been written, with the addition 
of a comma after the word John} 

^ The class had gone through a regular course of instruction on the 
nature of the sentence, and knew in theory all about sentence making, 
and the distinction between a sentence and a mere phrase. The pur- 
pose of the lesson, therefore, was not so much to communicate new 
ideas as to give a meaning to ideas already known, and to increase 
their presentative activity by co-presenting them to the consciousness 
in their proper connections. 

G 



82 EXPOSITION AND ILLUSTRATION IN TEACHING 

Teacher. Now what did John do ? 
Pwpil (confidently). Broke the window. 

T. Then what did ly/io do ? 

P. Broke the window. 

T. Were there two windows, then ? - 

P. No, sir. 

T. Then who broke it ? 

P. John. 

T. And what did who do ? 

P. (doubtfully). It says ^who broke the window.* 

T. Did it take two to break the window ? 

P. No, sir. 

T. Then which of them did the breaking ? 
(Pupils puzzled. No answer.) 

T. How many people were there altogether ? 

P. (cautiously). John and who. 

T. Now, which was bigger, John or who f 

P. They're both the same. 

T. Then there was only one person there ? 

P. Yes, sir. 

T. And what was his name ? 

P. John. 

T. And what did he do? 

P. Broke the window. 

T. Then, would it not be enough to say, ' John broke the window ' ? 

P. Yes, sir. 

T. Is that what it says on the blackboard ? 

P. No, sir : it says, 'John, who broke the window.' 

T. And John and who are the same person ? 

P. Yes, sir. 

T. Then, they both have the same right to the verb ? 

P. Yes, sir. 

T. Which of them is nearer the verb ? 

P. Who. 

T. What mark is between John and the verb ? 

P. A comma. 

T. Now if only one of the two can claim the verb, which has the 
better right to it ? 

P. Who. 



MENTAL ACTIVITY 83 

T. And every noun and pronoun that is a subject must have a 
verb? 

P. Yes, sir. 

T. Then if who gets ' broke, ' what verb is left for John f 

P. None. 

T. How many subjects are there here ? 

P. Two. 

T. And how many verbs ? 

P. One. 

T. And every subject must have a verb ? 

P. Yes, sir. 

T. How many verbs do we need, then, besides ' broke ' ? 

P. One. 

7^. Give me one. 

(No answer.) 

T. John (who broke a window) did something, or was something. 
What would you do if you broke a window ? 

P. (promptly). Run away, sir.^ 

T. Finish it, then. John, who broke a window ? 

P. Ran away. 

T. Which are the two verbs now ? 

P. ^Broke'and'ran.' 

T. Which belongs specially to who f 

P. Broke. 

T. And to John? 

P. Ran. 

In this and in all other applications of the Socratic 
method the teacher is really leading, though he seems 
to be following. He knows from the beginning the goal 
he desires to reach. He knows, further, the ideas the 
pupil already possesses, and feels that it is his business 

^ In the actual lesson this answer led to the inevitable moral rebuke 
from which the teacher returned to the main subject as above. As a 
matter of fact the teacher was severely criticised for not substituting 
in the final part the moral " paid for it, " instead of the discreditable 
"ran away." It does seem a pettifogging distinction, but I am in- 
clined to think the critics are right. 



84 EXPOSITION AND ILLUSTRATION IN TEACHING 

SO to manipulate those ideas that they shall ultimately 
form the combinations he desires. 

But when we say that the pupil possesses certain 
ideas, we do not mean that these ideas are necessarily 
present in the consciousness of the pupil when the les- 
son begins. At any moment in a given mind only a 
very limited number of ideas can be functioning. The 
mind is capable of being conscious in a great variety of 
ways, but is not capable of being conscious in all those 
ways at one and the same moment. When we say that 
a mind possesses a certain idea, we mean that that mind 
has a permanent potentiality of acting uniformly under 
certain identical conditions as often as those conditions 
recur. An idea not in consciousness may therefore 
be regarded as a permanent possibility of appropriate 
response to certain stimuli. 

The field of consciousness is limited, and unless an 
idea happens to be within that field at a given moment 
it would seem to be powerless, and indeed practically 
as if it did not exist. While we are thinking at this 
moment about consciousness and activity, myriads of 
ideas that in ordinary speech we may be said to possess 
are lying dormant, and exercise no influence upon the 
ideas that are at present in consciousness. Our ideas 
about rock crystals, for example, are as if they had no 
existence. But the important point has to be consid- 
ered : Are all our ideas that are not within consciousness 
at a particular moment equally inert? When a man is 
thinking of the power of ideas, for example, are his 
ideas about rock crystals and his ideas about John 
Locke equally ineffective ? He is not thinking about 
either Locke or crystals, but we have the general feel- 
ing that Locke is nearer to his thoughts at the present 



MENTAL ACTIVITY 85 

moment than are the crystals. Though Locke is below 
the threshold of consciousness he somehow seems nearer 
that threshold than do the crystals. Is there then a 
differentiation among the ideas that are out of con- 
sciousness corresponding to the differentiation we have 
seen to maintain within consciousness? It would 
seem that between the conscious and the unconscious 
there is a clear dichotomy. We are either conscious 
of an idea or we are not; anything that is below the 
threshold is therefore out of consciousness. Perhaps 
our trouble arises from a too rigid application of our 
figure of the threshold. There is something extremely 
definite in the idea of a threshold. A visitor either has 
or has not crossed it. He is either in our house or he 
is not. But if we are expecting him, or if we chance to 
see him coming up the walk we are influenced by him 
before he is actually in the house. The figure is not 
perhaps a very illuminating one, as it amounts, after all, 
to an illustration of consciousness by an appeal to con- 
sciousness. But since it is impossible to transcend 
consciousness, it is difficult to see how this community 
of subject-matter can be avoided. 

Even if we could justify the rigidity of the threshold 
figure, there would still remain a certain vagueness 
about the mental content in the marginal area. Ideas 
are in constant motion about the threshold of conscious- 
ness : now on the line, now above, now below. An idea 
that is at the present moment below the threshold, but 
a moment ago was above it and in another moment will 
be above it again, may be said to exercise a certain 
influence on the continuum on the borders of which it 
wavers. It is to meet cases of this kind that the term 
subconscious is used. Of course an idea must either 



86 EXPOSITION AND ILLUSTRATION IN TEACHING 

be in consciousness or not; accordingly we must regard 
a subconscious idea as in some way or other within 
consciousness. Yet from the way in which the term 
is used one would almost be led to think that it meant 
that certain ideas are in the consciousness without our 
being conscious of them — a clear contradiction in 
terms. By the Law of Excluded Middle there seems 
to be no place for the subconscious between the con- 
scious and the unconscious. Yet it is obvious that 
there is a difference between an idea that is hovering 
on the verge of consciousness, and one that is lost in 
the limbo of unconsciousness and may never again 
return to consciousness. Logic may rule out the sub- 
conscious, but Psychology must find it a place. 

To begin with, it has to be admitted that ideas that 
are not present in the consciousness exercise a certain 
influence upon ideas that are in the consciousness, and 
if an absolute distinction is demanded, it may be satis- 
factorily put for practical purposes as : At any given 
moment an idea may be said to be subconscious if 
without being itself within the consciousness it exercises 
an influence on ideas that are at that moment within 
the consciousness. It is easy to see that an idea that 
has just left the consciousness may leave behind it an 
influence that does not cease the moment it passes over 
the threshold. So with an idea that is coming up 
towards consciousness, it may not be very difficult to 
persuade people that it may cast its influence before it, 
and thus to some extent act within the mind before it 
appears. But we must go further, and admit that ideas 
may exercise an influence within the mind even if they 
do not reach the consciousness at all on the particular 
occasion that we examine. When we are dealing with a 



MENTAL ACTIVITY 87 

difficult and complicated problem, for example, we call 
into the consciousness a large number of relevant ideas 
and carefully examine them in relation to each other, 
and to the problem we are working with. But as we 
shall see more fully later ^ we cannot at will recall all 
the relevant ideas. By skilful manipulation we may 
gather together most of the significant ideas, but some 
at least remain outside consciousness. Are these un- 
called witnesses without influence on our decisions? 
The answer would appear to be that ideas in the sub- 
conscious region do exercise an influence upon ideas 
within consciousness, even though on the occasion in 
question they do not emerge at all above the threshold. 
The mind is dealing with a knotty problem in some 
such dangerous subject as Political Economy — noted 
for its pitfalls. The ideas at present in the continuum 
seem to fit into each other quite naturally; there is 
therefore internal harmony, and the problem seems to 
be solved. Yet the mind is not satisfied. It has an 
uneasy sense that there is a flaw somewhere, and goes 
on calling up all the available ideas connected with the 
subject in order to discover some possible error. For 
long nothing adverse turns up; but by and by an idea 
rises above the threshold and breaks down the hypoth- 
esis that was in all other respects satisfactory. This 
belated idea may be reasonably supposed to be sub- 
conscious at the time that the hypothesis was formed, 
thus causing the disquieting vague impression. Fur- 
ther it would have been none the less subconscious even 
if it had not come up in time to break down our hypoth- 
esis, or had never come into the consciousness at all. 
It might quite well have caused the uncomfortable 

1 P. 104. 



88 EXPOSITION AND ILLUSTRATION IN TEACHING 

feeling in the mind without coming up in time to warn 
the thinker. When the thinker's critics point out the 
flaw, the subconscious idea rises into consciousness 
and the thinker recognises that it had given him a 
vague warning though it did not reach his conscious- 
ness in time to prevent the blunder. 

The phenomena of the subconscious may be readily 
correlated with certain of the theories of brain action. 
If the associations formed among ideas correspond to 
interrelations established among certain neural systems 
through their functioning in a systematic way in re- 
sponse to certain stimuli, it may well be assumed that 
when certain systems are stimulated to the necessary 
extent, certain corresponding ideas rise into the con- 
sciousness. This stimulation has the natural tendency 
to spread among the other systems, but naturally it will 
spread more easily among systems correlated with ideas 
that have formerly been connected with the ideas at 
present in consciousness. It may plausibly be sug- 
gested that within the brain there is a sort of physical 
replica of the field of consciousness; certain neural 
systems are in a high state of excitement — these cor- 
respond to the focal ideas. Systems in various de- 
creasing degrees of excitement may well correspond to 
the various degrees of obscuration of the ideas till 
tracts are reached that, though stimulated by the gen- 
eral impulse that affects all the system we are dealing 
with, are not sufficiently stimulated to cause a definite 
idea to rise into consciousness. Such tracts will corre- 
spond to the ideas that are in the subconscious state. 
If the neural system concerned is thoroughly well 
organised, as must be the case with regard to the sj^s- 
tem that regulates our thinking on any subject of which 



MENTAL ACTIVITY 89 

we have an intelligent knowledge, it will be impossible 
to stimulate some of the tracts up to consciousness 
pitch without at the same time stimulating all the cor- 
related tracts into some degree of activity. Accord- 
ingly, even the most remote relevant ideas will be raised 
to at least the subconscious state, and the whole system 
so energised that its elements require only a very slight 
additional impulse to send them up into consciousness. 

This additional stimulus is what we seek to give them 
by our ordinary methods of dealing with problems. 
We put ourselves in the way of stimulating certain 
ideas. We turn to books where we know such ideas are 
treated. This gives us the primary set of ideas. The 
systems corresponding to these primary ideas stimu- 
late a great many other systems at the secondary and 
tertiary degrees of remoteness. If our system of ideas 
is perfectly coordinated, then the neural tracts will 
inevitably be stimulated in their proper order and the 
corresponding ideas will present themselves to con- 
sciousness, just as they are required for purposes of 
thought. This indeed is what happens in well-regulated 
minds when dealing with subjects in which they are 
quite at home. 

It goes without saying that this parallelism between 
the physical and the mental in no way commits us to 
materialism. Even if we could correlate every idea 
that passes through the mind with a definite corre- 
sponding cell in the brain, we would be no nearer than 
we were before to the solution of the problem of the 
relation between mind and matter. The physical 
parallel has been introduced here mainly because it gives 
a certain confirmation of the view taken with regard to 
the place of the subconscious in mental process. If 



90 EXPOSITION AND ILLUSTRATION IN TEACHING 

the theory adopted with regard to the subconscious 
fits in with the hypotheses of certain physiological 
psychologists, there is the greater likelihood of its 
being true. In any case the analogy serves as a useful 
illustration, and after all, if analogy is not always itself 
a reliable argument, we are told that it often indicates 
that a reliable argument exists. 



CHAPTER IV 

Mental Backgrounds 

Painters are familiar with the phenomena of what 
they call Turbid Media. Colours vary according to the 
colour tone of the material upon which they are laid. 
This is what the Hon. John Collier has to say on thfe 
subject: — 

" Rub a little ivory black thinly over a white canvas, it will ap- 
pear a distinct brown ; mix the same colour with white, it becomes 
a neutral grey ; brush this grey thinly over a black ground, it will 
have a distinctly bluish tinge ; so that the same pigment can vary 
from a warm brown to a blue grey without admixture with any 
other colour but white, merely in accordance with the manipulation 
it receives. Yellow ochre gives similar results ; when lightly brushed 
over a white ground it seems a rich orange, when brushed in pre- 
cisely the same way over a black ground it seems a sort of green." 

So with the mind. The same idea has to harmonise 
itself with quite a different tone according to the nature 
of the background against which it is projected. The 
groups of ideas that give body to the stream of con- 
sciousness may be, without too violent a figure, com- 
pared with a background, which like every other back- 
ground has a powerful influence on our view of any 
element worked into the foreground. Naturally the 
analogy is more complete when we deal with the af- 
fective aspect of thought or speech. Public orators 
of a sentimental turn are not uncommonly guilty of 

* Primer of Art, p. 59. 
91 



92 EXPOSITION AND ILLUSTRATION IN TEACHING 

falling into a rhapsodical mode of expression, a sort of 
'^Ah!" strain, that renders them blind to the real mean- 
ing of the ideas they use. The emotional background 
is too strong for the ideas that are projected against it. 
Next morning in cold blood the orator usually sees his 
mistake; indeed there is a danger that the cold daylight 
criticism may go too far in the other direction, for 
it has always to be remembered that there are occa- 
sions when the value of an idea must not be judged too 
closely by the logical standard. Still there is some- 
thing wrong when the emotional background retains 
its paralysing power even through the callous period 
of proofreading. The following occurs at the end of a 
sermon-tale to children by a well-known London clergy- 
man, who published it along with other sermons in 
book form in 1891. 

"And away down in 81st Street a woman was stitching what 
seemed like a httle nightgown, but ah me ! it was not that — it was 
something sadder still, for her little dear baby had died; and the 
mother's heart was full, and the tears would flow." 

Apart from the background of this sad sermon-tale 
no one would think that '^a little nightgown" was a 
.particularly sad object, only less sad, in fact, than a 
little shroud. Yet so powerful is this background of 
sentiment, that not only did it blind the preacher at the 
time, but completely deceived two different classes of 
divinity students to whom I had occasion to lecture, 
and upon whom I took the liberty to experiment. 
My subject was the preparation of sermons for the 
young, and I read the passage — naturally beginning a 
little bit before the dangerous passage in order to give 
the background its proper effect — to illustrate a 
psychological principle. In both cases the implicit 



MENTAL BACKGROUND 93 

absurdity escaped detection, though, when it was 
pointed out to them, the young men were much cha- 
grined that they had allowed it to pass. 

But the figure of a background in mental matters 
is not limited to the affective tone. It has a useful 
application on the ideational plane. We have found 
that each idea that occurs to the mind must make itself 
at home there. It must harmonise itself with its sur- 
roundings; and must take a different meaning accord- 
ing to the mental background against which it is pro- 
jected. The presented content may be quite neutral 
or it may have a positive tone of its own. In both cases 
the new idea or ideas must submit to a modification of 
tone or meaning from the effect of the background. 

Take some such colourless sentence as Think of him, 
and note the difference effected by projecting it against 
the following backgrounds. 

A picture in Life of a low-class photographer trying to encourage 
a pleasant expression on his female sitter's face. 

A widow laying flowers on a grave and addressing her little girl. 

A religious revival meeting. 

A French schoolmaster during the Franco-Prussian war pointing 
to a portrait of the first Napoleon. 

A conspirators' meeting where a traitor's name has been men- 
tioned. 

A crowd of starving " unemployed " watching the Mayor pass from 
his carriage to a City Banquet. 

The same thing applies to an idea dealing with a con- 
crete object, say a fish. Note how the emotion aroused 
varies according to the background. Against a back- 
ground that includes the Early Christians and the 
Catacombs it arouses either a deeply religious or a 
mildly antiquarian interest. Try it now against a 



94 EXPOSITION AND ILLUSTRATION JN TEACHING 

background of Astronomy, Sport, Bread-winning, 
Geography, Art, Science, Slang, Heraldry, Asceticism. 

Most of the honest, that is, unmalicious, misunder- 
standings of life, are the result of failing to make al- 
lowance for the background in the mind of another. 
When the same ideas are presented against different 
backgrounds, the consequent confusion is so inevitable 
that common speech includes a special phrase to ex- 
press this particular form of misunderstanding. When 
people are at '^ cross purposes, '' they are dealing with 
the same words in different connections, which is the 
same as saying that the meanings are modified by the 
backgrounds. Here we have passed beyond mere tone, 
and have reached the region of relation among the ele- 
ments that make up the content of mind. The care- 
less, unreflective man takes it for granted that the idea 
he sends forth from a given background will find a cor- 
responding background in the mind of his hearer or 
reader. Fortunately his expectation is usually jiisti- 
fied. By the very fact that two minds are in com- 
munication, they are placed in such a relation as to 
encourage the development of the same backgrounds. 
But at the very beginning of a conversation there is 
sometimes a little difficulty. The preliminary talk 
between two persons, before coming to the real point, 
is a sort of tuning up, a kind of mental feeling for the 
proper pitch. This preliminary talk has sometimes 
been compared to the few passes that a pair of fencers 
make before coming to the real business of the en- 
counter. But the figure of finding the pitch is perhaps 
nearer the truth. 

Many people — particularly young people — are 
irritated at what they call ^'beating about the bush." 



MENTAL BACKGROUND 95 

No doubt the principle in medias res is admirable, 
if we are sure that we and our interlocutor are to be in 
the middle of the same res. If two men meet to 
discuss the same subject, they are probably provided 
with the same backgrounds, or at any rate closely 
similar backgrounds; but even then a certain amount 
of harmonising may be necessary. It is quite possible 
that each may view the subject against a background 
quite differently made up, though composed of the 
same elements. People who argue for the sake of 
arguing, people who write to the newspapers, almost in- 
variably deal with ideas in the light of their own back- 
grounds, and refuse to take the trouble to discover the 
mental backgrounds against which the same ideas are 
projected in the mind of the person with whom they 
debate. If we desire to convince another person that 
his view is wrong, we must endeavour to find out exactly 
what that view is; we must discover what sort of back- 
ground his ideas are projected against. 

The reason why we are so seldom at cross purposes 
is that we rarely move out of our own set. All societies 
are made up of sets or coteries, each of which is marked 
by the possession of a common series of backgrounds. 
In dealing with those of our own set we have no diffi- 
culty, and dealing with our own set makes up the 
greater part of life for most of us. It is when we have 
communication with our political opponents, with 
members of a different church, with foreigners, even 
with members of some of the ordinary ^' Anti'' societies, 
that we realise that our ideas do not seem to have the 
effect upon our interlocutors that we intend. 

Teachers in a more or less conscious way feel the 
need of bringing their own backgrounds into harmony 



96 EXPOSITION AND ILLUSTRATION IN TEACHING 

with those of their pupils. Young teachers in particu- 
lar soon discover that their questions do not produce 
the answers they were intended to elicit. A question 
is asked, for example, the answer to which is known 
to be within the range of the pupil's knowledge. There 
is no doubt about the matter. The teacher knows, from 
immediately preceding experience, that the answer is in 
the pupil's mind only waiting to be drawn out. Indeed 
the question may be fairly regarded as nothing more 
than a stage in the process of making clear and distinct 
an idea that the pupil already possesses, though in a 
vague way. The question is, however, so expressed that 
the pupil, with the best intention in the world, cannot 
discover against which background he is expected to 
project the ideas concerned. Accordingly he projects 
them against the first available background, in the hope 
that this may be the right one. 

^^ Where was St. Paul converted?" asks the teacher, 
speaking from a geographical background. ^^In the 
ninth chapter of the Acts," responds the pupil, from 
a background of textual reference. In testing the in- 
telligence of a class the inspector asks, ^' Where do you 
find gates?" The pupil, from a background made up 
of puzzling experiences of the Socratic method, answers : 
''We don't find gates, we make them." From an his- 
torico-geographical background the inspector desired to 
elicit the deleterious effect of a large town on the purity 
of a river. He brought out the fact that Robert the 
Bruce spent his latter years at Roseneath on the Clyde 
in Scotland, and that as a recreation he very probably — 
according to the inspector — fished in the river. The 
question that was to incriminate those who were re- 
sponsible for the pollution of the Clyde took the form : 



MENTAL BACKGROUND 97 

''Why couldn^t the Bruce fish there now?'' From 
a background of plain common sense came the reply: 
''Because he's dead." 

It is manifest that what we are here calling mental 
backgrounds correspond to what we have already 
spoken of as continuums ; but we are now treating them 
from a new point of view. Hitherto we have been con- 
cerned with the relative clearness or obscurity of the 
elements that make up the continuum; now we are 
interested in the varying effects of the same idea ac- 
cording to the continuum in which it is found. Instead 
of considering the effect of the diffusion and concentra- 
tion of consciousness on the composition of the con- 
tinuum, we now examine the change produced on a 
given idea by the company in which it finds itself. 
The management of mental backgrounds is clearly 
an important part of the process of Exposition: ac- 
cordingly we must study the mechanism of these back- 
grounds; we must look into the problem of mental 
scene-shifting. 

With regard to the elements out of which the back- 
grounds are worked up there is probably a greater uni- 
formity than would at first sight be expected. The 
ultimate elements, the products of sense-perception, 
are practically uniform, though no doubt even here 
there are differences corresponding to the physical con- 
ditions of the sense organs. But even admitting the 
general uniformity of elements there remains a vast 
possibility of differentiation through variety in com- 
bination. Given a hundred minds with precisely the 
same ideas as presented content, it is probable that no 
two of them have the ideas arranged in the same way. 
The order in which the ideas were originally presented, 



98 EXPOSITION AND ILLUSTRATION IN TEACHING 

and the circumstances of the different persons con- 
cerned, have brought about a necessary variety in the 
combinations. It is obvious that it is impossible to 
make a classification of minds on a basis of mental con- 
tent without practically attempting to ^^ exhaust the 
universe/' though a rough and ready classification may 
be very serviceable for practical purposes/ But with 
respect to the mechanism by which combinations are 
effected there need not be the same difficulty. Minds 
may be divided into three classes according to the 
degree of stability they establish among the elements as 
components of complexes. Naturally there are certain 
complexes of ideas that are formed to correspond to 
certain complexes of objective phenomena. These 
complexes owe their stability to the uniformity with 
which they react satisfactorily upon the conditions of 
actual experience. But certain other complexes de- 
pend for their stability upon the quality of the mind in 
which they are formed. 

From this point of view the first kind of mind may 
be named the rigid. It is marked by the close connec- 
tion that is maintained among the elements that go to 
form a given background. Instead of moving freely 
among themselves the individual ideas form a complex 
once for all, and can hardly be separated from each 
other. The rigidity may result from the emotional 
tone; we may refuse to break up our complex because 
we prefer to have the elements arranged in that way. 
This is the case with the stubborn little cottage girl 

^ Such studies as Dr. Berthold Hartmann's Die Analyse des kind- 
lichen Gedankenkreises als die naturgemdsse Grundlage des ersten 
Schulunterrichts (Leipzig, 1896) show that a good beginning has al- 
ready been made in this kind of classification. 



MENTAL BACKGROUND 99 

who in Wordsworth's poem refused to break up the 
combination of herself and her brothers and sisters into 
a group of seven, merely because two of them were 
dead. The poet does his best to break up the com- 
plex: — 

" ' But they are dead ; those two are dead ! 

Their spirits are in heaven ! ' 
'Twas throwing words away ; for still 
The httle maid would have her will, 

And said, ' Nay, we are seven ! ' " 

The extreme case of this rigidity is to be found in that 
form of insanity that bears the name of Videe fixe. 

Very frequently the natural tendency of certain minds 
towards rigidity is intensified by bad teaching, teaching 
for the sake of immediate results rather than for the 
sake of the power that comes from the organization of 
ideas. It seems to save time to present ideas in ready- 
made boluses. Education, however, should be free from 
the trammels of such time conditions. The ultimate 
result is the only thing worth considering. We are not 
here concerned with the practical difficulties of supply- 
ing the best possible equipment for life's work in the 
limited time at the disposal of the teacher in the case 
of the average child. Few questions are of greater 
importance than that of making the most of the short 
school time available for the artisan class. But at 
present our aim is to get at the best ideal state. Once 
this has been determined, educators may be in a posi- 
tion to discuss what compromise, as a compromise 
between what ought to be and what is, will lead to the 
best result. Obviously we must know the best possible, 
before we can examine how closely we can approach it 
without attempting to overstep the limits of our powers. 



100 EXPOSITION AND ILLUSTRATION IN TEACHING 

The backgrounds formed by rigid minds may be 
termed fixed. Naturally no background can remain 
permanently fixed, except perhaps in the case of the 
insane, but in ordinary life we find modified forms of 
Videe fixe. Your dull, matter-of-fact man regards all 
things of the same class against the same unvarying 
background. He finds the greatest possible difficulty 
in knowing what nimbler-witted people mean. The 
same ideas are presented to him and to them. He can- 
not understand why they produce such a different effect 
in the two cases. 

We shall see later that up to a certain degree of elabo- 
ration, it is a distinct advantage to have fixed complexes 
of ideas, but beyond that degree fixity is a thing the 
teacher must fight against. In the case of rigid minds it 
is obviously of prime importance that the first presenta- 
tion of a given complex of ideas shall be properly made, 
since any change at a later stage will be exceedingly 
difficult. To prevent the evil effects of rigidity, then, 
the best means is to present the component elements in 
as simple a form as possible. This does not mean 
merely in the easiest forms, but as nearly as may be in 
the forms resulting from ultimate analysis. The mind 
we appeal to ought to do its own combinations. It 
does not, of course, follow that the mind we deal with 
will form a different complex from that we have our- 
selves formed. The skilful teacher will in fact manipu- 
late his facts so that the pupil will form precisely the 
same complex as the less skilful teacher would present 
as a ready-made bolus. But the fact that the bolus-fed 
pupil and his better-taught compeer form the same 
final complex, in no way proves that the resulting know- 
ledge is of the same value in the two cases. There is a 



MENTAL BACKGROUND 101 

fundamental psychological difference between ideas 
grouped by the mind itself, and the same ideas in the 
same grouping when that grouping has been presented 
ready made as the result of the operations of another 
mind. It is true that even when the mind has made 
its own complexes of ideas, there may be unhealthy 
rigidity in the result. Some minds are naturally in- 
elastic. That class of mind that Roger Ascham calls 
harde wittes ^ is inclined to be unduly rigid. Great 
care must accordingly be taken that the true complex 
should be suggested at an early stage, and further, 
continual exercise should be given in dealing with the 
same ideas in different connections. Exercises of all 
kinds have their uses in this way. Every time that the 
teacher is able to satisfy the reproach that is implied in 
the complaint ^'But you said so-and-so, '^ he is loosening 
the too rigid bonds that unite ideas. 

After all, harde wittes form capital material for the 
teacher to exercise his skill upon, and it is not difficult 
to see that old Roger has a warm side to this class of 
pupil. But every teacher dislikes the opposite type of 
mind that, for want of a better name, may be called the 
fluid. In this case there is no fear of too close a con- 
nection among the ideas that form a background. 
They are allowed to roll about in the mind pretty much 
as the molecules of a liquid mingle with each other. 
Some complexes must, of course, be maintained in a 
position of comparative stability, else the mind would 
fall to pieces altogether. But the complexes are at any 
time easily broken up. To this type of pupil one com- 
plex is as good as another. But even here we must 

^ The Scholemaster : The first booke tep.chyng the brynging up of 
youth. Arber's Reprints, p. 34. 



102 EXPOSITION AND ILLUSTRATION IN TEACHING 

try to get the mind to do its own combining and building 
up. No doubt we shall have to use stronger induce- 
ments, and we must find better and firmer bonds. 
Above all we must keep on repeating those connections 
that we seek to impress on the pupil-mind. Instead 
of seeking out exercises in which the individual ideas 
are exhibited in different connections we must confine 
ourselves to those that illustrate the working of the 
ideas in the same connection though under different 
aspects. The complex must as before be made by the 
pupil himself; but, once made, it may be greatly 
strengthened by the outside influence of the teacher. 

The fixed background is in general more character- 
istic of mature life; the unstable background is common 
in school. The necessity of childhood to grow as well 
as to live makes it imperative that material for growth 
should be gathered from all parts. Accordingly it is 
an arrangement of nature that children should be rest- 
less in body so as to secure an all-round physical de- 
velopment, and restless in spirit in order that they may 
derive materials from all their environment. A child 
may have a more or less strong inherent tendency to 
develop fixed backgrounds, but at early stages it is 
unusual to find this tendency very prominent. Our 
great difficulty is the instability that characterises 
the youthful background. We are never quite sure 
that the ideas of this minute will be projected against 
the same background as the ideas of last. Among 
grown-up people those who are silly, giggling, flippant, 
are usually those with unstable backgrounds. What 
is often called the Associative mind is of this class. 
No doubt the force of association tends to make ideas 
cohere. But in the case of fluid minds association 



MENTAL BACKGROUND 103 

exercises its power rather in promoting a flow of ideas 
than in consoUdating ideas into organised groups. 
A word is enough to divert the stream of thought. 
Dame Quickly is the emeritus example of a mind of this 
sort — though, unfortunately, we do not need to go 
so far afield for abundant examples of the type. The 
background against which the ideas of Dame Quickly 
project themselves can hardly be called stable. It 
is more like a rapidly moving panorama than an or- 
dinary picture. 

The third class of mind, as characterised by its back- 
grounds, is the desirable one that may be named the 
'plastic. This type of mind forms its own complexes 
with fair ease, and at the same time is able to retain 
them in that state that prevents deliquescence on the 
one hand and rigidity on the other. The resulting 
backgrounds are mobile. They remain steady as long 
as they are required to be steady, but are ready for 
immediate change if that is found desirable. They are 
stable enough to allow of very gradual change, and 
mobile enough to submit to sudden fluctuations if need 
be. Nimble-witted people are marked by a high degree 
of mobility of background. 

To illustrate the working of mental backgrounds, 
take the cases of a congregation listening to a sermon, 
students listening to a lecture, and a person reading a 
poem. In the sermon, as a rule, there is no call for vio- 
lent change of background. Frequently, indeed, the 
lines are laid out beforehand, the heads are given, and 
the work of the preacher is to develop these heads, the 
work of the listener to supply the appropriate and slowly 
changing background. So with the instructive lecture. 
Fact after fact is introduced, but for each fact a place 



104 EXPOSITION AND ILLUSTRATION IN TEACHING 

has been prepared. At the very start of the lecture 
the teacher, if he knows his business, has referred to 
some fact that he is sure Ues within the knowledge of 
his hearers. This prepares the way for a background 
different from that which previously existed in the 
students' minds. As a rule that previous background 
is not of much consequence. It is usually made up of 
floating ideas of the campus or stairs or notebooks or 
whittling pencils. If the students have just come from 
an examination, or from a college row, or even from 
a specially interesting lecture, the power of the back- 
ground they bring with them may be much greater, 
and much more difficult for the new lecturer to deal 
with. Under adverse circumstances like these, the 
teacher has two courses open to him. He may begin 
with a particularly striking sentence, in the hope of 
causing a rapid change of background, in which case 
he makes an assault upon the attention in the hope of 
taking it by storm. Or he may begin by saying noth- 
ing to which he attaches much importance during the 
first five minutes, in the hope that the old background 
will gradually give way, and enable him to establish 
a new one as soon as he begins to deal with the real 
matter of his lecture. This latter method is, on the 
whole, more likely to succeed. Replacing the old back- 
ground item by item is a much more hopeful proceed- 
ing than an attempt to wave the conjurer's wand. 
A background cannot be called up at will. Recall 
is not quite the same thing. It is perhaps not very 
difficult to reinstate the background of a previous 
lecture. Indeed, it ought to be easy, for all the help 
students usually get is the dry paragraph that follows 
the colorless opening: ^^ Gentlemen, in^our last lecture 



MENTAL BACKGROUND 105 

. . .'^ But a real beginning is different. Why is it 
that the experienced railway reader prefers to start his 
journey with a ^' begun'' novel? And if it is a little 
irksome to make a beginning of a novel, why is it still 
harder to begin to read a play ? The answer is clearly 
that in both cases there is no background, and that in 
the case of the play the background is more remote 
than in the novel, where the author at least does his 
best to help the reader in supplying a background. 

In reading a poem we are often called upon to make 
rapid and violent changes of background. This does 
not mean that we must suddenly change the whole 
body of thought that corresponds to James's stream. 
In reading a well-constructed poem, the main body of 
thought remains constant in spite of the rapid changes 
called for by the accumulated figures of speech. The 
as of the figure suspends the main interest of the reader 
till the corresponding so releases it again. At Virgil's 
invitation^ we leave the two Trojans and accompany 
him to the teeming bee-hive, but when the visit is over, 
we gladly return to ^neas and his friend. While we 
are with the bees, what has become of the Trojans and 
the Tyrians ? Has the background of country life dis- 
placed entirely the background supplied by the surging 
city? Are our thoughts with the bees or with the 
Trojans and the Tyrians? Different minds act dif- 
ferently here. The rigid mind prefers to remain with 
the Trojans and the busy city-builders: it resents this 
interruption, looks at the bees with disapproval, waits 
impatiently till the poet sees fit to return to his proper 
work. The fluid mind, on the other hand, accompanies 
the poet gladly, forgets all about the Trojans, and 

1 ^neid, Book I, 430. 



106 EXPOSITION AND ILLUSTRATION IN TEACHING 

revels in the new scene. The man of plastic mind read- 
ily supplies the new background that is necessary, but 
does not forget the old. His enjoyment of the new 
background is affected by the fact that it has a relation 
to the old one. The country scene has a different 
charm for him here, compared with what it would 
have had it occurred, say, in Wordsworth, where it 
would appear for its own sake. It is a case of turbid 
media. 

Some minds treat such temporary backgrounds as 
ends in themselves, others as a mere part of a wider 
whole. Some keep the Trojans before their minds all 
the while they are considering the bees. The interest 
for minds of this class lies mainly in the relation be- 
tween the two sets of ideas. The toiling Tyrians are 
set over against the busy bees. Other minds can sus- 
pend, for the time being, the background of Dido's 
new city without letting it disappear altogether. The 
charm of comparison comes after the figure has been 
enjoyed for its own sake. Yet even while the figure 
is present it cannot be treated quite as if it were an 
independent subject of thought. It lies on the sur- 
face of the stream of thought, it is true; it cannot be 
denied that it is focal, but the influence of the whole 
undercurrent of the stream is felt; the subconscious 
body of the stream influences our treatment of the 
surface current. 

It is in the practical affairs of life that there is a call 
for sudden and more or less complete changes of back- 
ground. The different business calls a man receives in 
his office every day need not involve a greater change 
of background than we have seen in the case of read- 
ing a poem. There is usually sufficient continuity to 



MENTAL BACKGROUND 107 

maintain the connection between the parts. But if a 
man is interrupted in his business by household cares, 
or by, say, church concerns, the difficulty of main- 
taining a stable background is greatly increased. A 
man called away suddenly, after a hard bargain with 
a business rival, to deal with a case of conscience can 
hardly make the necessary change of background with 
the required rapidity. In this case there has to be a 
complete change in the body of the stream of conscious- 
ness before the required background can be attained. 
What happens as a matter of fact is that at the beginning 
of the new interview there is a good deal of confusion of 
thought. The new background is not distinct. It is 
affected according to the laws of turbid media by the 
background that has not yet had time to disappear. 
After a little, thought becomes clearer, ideas are grad- 
ually rearranged, the old background becomes so dim 
as not to interfere with the new, and the change is 
effected. 

So far we have been dealing with backgrounds as 
wholes. But the elements that make up a given back- 
ground are not combined as simple and independent 
units. They are all grouped together more or less 
firmly into different complexes, and these complexes 
form the real units of combination. In all descriptive 
writing and speaking it is assumed that the reader or 
hearer has the necessary complexes at hand ready-made. 
The more cultured the audience with reference to a par- 
ticular subject the greater the degree of complexity the 
expositor is entitled to assume in the combination unit. 
When a novelist sets his scene in a medissval castle, he 
assumes that his readers have a complex of ideas that 
corresponds to his own. He does not begin with the 



108 EXPOSITION AND ILLUSTRATION IN TEACHING 

elementary ideas of portcullis, barbican, moat, draw- 
bridge, keep, bailey; he assumes these to be present 
and arranged in a particular way. If the novelist uses 
the words '' Norman castle," he assumes what he has 
assumed before, but limits the possible combinations 
of the elements. If he mentions the century in which 
the castle was built, he makes a still higher demand 
on his readers' ability to conform to standard in form- 
ing complexes. If the novelist thereafter feels called 
upon to expand into description, he concerns himself 
entirely with those parts of the castle in question that 
are more or less peculiar to it. As a matter of fact, 
we have all a large supply of ready-made complexes 
that are in themselves invariable and may be used as 
composite units to build up any desired whole. The 
skill of the poet, the teacher, and the novelist is shown 
in the way they manipulate these complexes to form 
the whole that suits their immediate purpose, 
i The first general remark to be made about these 
ready-made complexes is that they owe some of their 
characteristics to the preferred sense of the person in 
whose mind they are formed. It is well known that 
minds differ in the class of impressions that affect them 
most. There are those who depend mainly upon the 
eye. These are termed visuals.^ For them every- 
thing that is comfortably assimilated by the mind has 
been treated in terms of form, size, and colour. Audiles, 
on the other hand, prefer to deal with sounds. An 
audile enjoys being read to; a visual is unhappy unless 
he can read for himself. At the play the visual is most 
impressed by the scenery, the dresses, the gestures; 
the audile by the dialogue, the songs, the music. Those 

^ Some writers prefer the term visiles. 



MENTAL BACKGROUND 109 

that are known as tactiles reduce everything as far as 
possible to impressions of the sense of touch. When 
we speak of a cat, the visual has an impression of its size, 
form, and colour; the audile remembers its purring or 
its caterwauling; the tactile reproduces in his conscious- 
ness the pleasant feel of its fur. The senses of smell 
and taste are not usually included in this classification : 
we do not, as a rule, speak of gustatives or olfactives. 
This is probably because these senses are of inferior 
importance in the building up of knowledge. There is 
no doubt, however, that they also have a considerable 
effect in modifying the way in which different people 
regard the same thing. A caution is here not out of 
place. We must not make the distinction too promi- 
nent. It is not to be supposed that an audile gets most 
of his information through the ear, but only that that 
is the best way to get at that particular person. He 
prefers to have his knowledge come through the ear. 
It is quite possible that the psycho-physicists may by 
and by be able to arrange the senses in their precise 
order of merit as knowledge-providers. But even if 
this absolute order of merit were to be published to- 
morrow, it would in no way affect the fact that people 
have their preferred sense. An audile may learn abso- 
lutely more from the sense of sight than from the sense 
of hearing, and be an audile none the less. 

In dealing with mental backgrounds most of us have 
the prevailing impression of sight. For this there are 
obvious reasons. There are more visuals than audiles 
in the world; and in addition, the very word back- 
ground drives us by association to visual impressions. 
Moreover, for the purpose of school, visual back- 
grounds are more useful than any others, for the very 



110 EXPOSITION AND ILLUSTRATION IN TEACHING 

sufficient reason that we can, to some extent at least, 
compare them with each other through the intermediary 
of an external standard. If the pupil is asked to think 
of a country town, a picture at once rises in his mind. 
This is his picture of a country town. If it is analysed, 
it will be found in all probability that it owes most of 
its characteristics to one particular town with which he 
is familiar, or in connection with which he made his 
first acquaintance with country towns. Further, the 
fewer country towns the pupil has seen the clearer is 
the picture that rises in his mind. To one who has seen 
a great number of such towns there is a vagueness about 
the picture. The peculiarities of the different towns 
are contrary ideas, and therefore arrest each other. 
Accordingly there is a struggle going on all along the 
line, and only the absolutely common elements remain 
clear. If, now, the man of many country towns is 
determined to have a clear picture, he can usually suc- 
ceed; but the price that he pays is the loss of the pic- 
ture of a country town in general, and the adoption 
of a particular town. His town is the pictured image 
of what he has actually seen. Indeed this is the most 
common form. Instead of having a vague background 
ready-made, most people have more or less vague mem- 
ories of backgrounds that actually exist. At first sight 
it may seem that there is no harm in this, and some 
may even be prepared to say that these pictures are 
better than vague generalised outlines. But when 
it comes to supplying backgrounds to ideas presented 
by another, it will be found that misunderstandings 
are apt to arise from the detailed character of the pic- 
ture. The teacher's exposition may not fit into the 
pupil's picture because some detail in that picture is 



MENTAL BACKGROUND 111 

inconsistent with something the teacher has said. This 
detail is not essential to the general background de- 
manded by the teacher, and should therefore be elim- 
inated. In a description, for example, the teacher 
may speak of the church as being on the north of the 
market-place, while in the pupil's picture it is on the 
east. The pupil's mind resents this, and a wrong atti- 
tude results. With a purely generalised picture of the 
village the church can be put anywhere without rous- 
ing opposition. 

A very interesting as well as useful exercise is to take 
the catalogue of an art exhibition before seeing the 
pictures, and try to realise what sort of picture corre- 
sponds to each of the descriptive titles. The man of 
many galleries succeeds fairly well. His mental picture 
of even such a tantalising description as '^Portrait of 
a Lady" is not usually far wrong. But to the ordinary 
lay mind there will be little but disappointment. 
^^Chill October," ^^With Daisies Pied," ^'In Spate," 
''Where the Bee Lurks," ''Boors Drinking," "The 
Village Wedding," all raise pictures in our minds that 
do not correspond to what we find in the frames. 
Yet we cannot blame the painters: in each case we 
are constrained to admit that the picture justifies the 
name, and in most cases we are prepared to acknow- 
ledge that the painter's idea is better than ours. But 
for all that, the two pictures, his and ours, are not 
the same. So with description. However carefully a 
town may be described to you, — in words, — you will 
always find that when you reach the town itself it is 
not quite what you had pictured it to be. You cannot 
accuse your friend of describing it falsely or carelessly. 
Everything he has told you is justified by what you see. 



112 EXPOSITION AND ILLUSTRATION IN TEACHING 

You admit that it is exactly as he described it to you — 
only it is different. 

Now if practical issues depend upon this description, 
how easily you might be misled. Your picture corre- 
sponds at all the points of contact with the description, 
but at all other points your picture is independent of 
the reality, and has no guidance. Let us not forget 
that the very vagueness of our backgrounds may have 
its use. It is this quality that enables us to fit them 
into so many different frames. If any discrepancy 
arises, it can be readily remedied, while as for the remain- 
ing unexpressed details they do not matter, so long as 
they do not imply a hidden contradiction. We some- 
times forget how much work the reader or hearer has 
to do as the apparently passive partner in the process 
of Exposition. The writer no doubt brings his ideas 
together and lays them before us with more or less skill ; 
but the reader has to supply his own backgrounds, and 
see that they agree with the ideas projected against 
them. Sometimes it happens that a discrepancy 
arises because in the mind of the writer the idea was 
originally projected against a false background, and 
the error is detected against the more accurate back- 
ground supplied by the reader.^ More frequently the 
reader's faulty background is exposed by the process 
of projecting the writer's ideas against it. A schoolboy 
who had never been in Edinburgh objected to his lesson 
book for describing an attempt on Edinburgh Castle 
made from the steep cliff on the west side. His argu- 
ment was that the steep cliff was on the east side. 
When asked to justify his criticism, he had nothing to 
say but a reiteration that the account must be wrong; 

^ This is worked out in greater detail in Chap. XIV, p. 344, 



MENTAL BACKGROUND 113 

this seemed to him self-evident. It was only when 
hard pressed by his teacher, who pointed out that the 
access was quite easy from the east, that the boy scorn- 
fully explained that climbing a high cliff out of small 
boats was not what he considered an easy approach. 
The mention of boats led to further enquiries, when 
it came out that the boy was dealing with the only 
castle he had seen, which happened to be Dunnottar 
Castle in the northeast of Scotland, where certainly 
his objection held. He had simply taken the word 
castle to connote all the elements of the single castle 
he had seen. 

Apart from the errors arising from different concep- 
tions of the content of the mental backgrounds, there is 
another source of danger. Exposition may fail because 
of what may be called mental parallax. The teacher 
and the pupil may project the same ideas against identi- 
cal backgrounds and yet come to different conclusions, 
because they view the ideas from different standpoints. 
The teacher may project a given idea against one part 
of the background, and the pupil against another. 
Much depends upon the point of view. Nothing is 
more important in Exposition than the selection of the 
proper point of view and the securing of the coincidence 
of the pupil's standpoint with the teacher's. 

The danger of a wrong point of view may be illus- 
trated from our own adult experience when reading 
novels. Sometimes the author takes it upon him to 
keep us for several chapters in the company of the vil- 
lain and his accomplices. Gradually we begin uncon- 
sciously to look at things from the villain's standpoint. 
There is, of course, in this case no real harm done; it 
is only a matter of tone. But the effect is quite per- 



114 EXPOSITION AND ILLUSTRATION IN TEACHING 

ceptible. By and by, when some virtuous person in 
the story comes along and interferes with the villain's 
plans, we experience a distinct, if momentary, an- 
noyance/ 

It must not be supposed that the point of view is 
limited in its effects to the tone value of a lesson. It 
is equally important in Exposition that deals with the 
cognitive side. In the more practical parts of our 
teaching, in which imitation is largely reHed upon, we 
find the point of view of the first importance. In the 
various exercises in which the teacher shows the pupils 
by example exactly what they are to do, there is a 
special form of confusion that arises from difference 
in the point of view. This is the distinction between 
right and left. In ordinary Hfe it is common to find a 
certain amount of confusion between the right and 
the left. Every stranger who asks his way in a great 
city has abundant evidence of the existence of this con- 
fusion. It is always well to test each direction at every 
turning. For 'Hhird turning to the right" we have 
frequently to read 'Hhird turning to the left." This 
arises partly from the confusion that inevitably occurs 
in an appreciable percentage of cases when we are 
dealing with two opposed directions. We have the 
same confusion to a less degree between east and west 
on a map, but not nearly so frequently between north 
and south. There may be other causes for the differ- 
ence, but there can be little doubt that east and west 
are more readily confused because of their connection 
with the right and left of the map. 

The fact that the wayfarer and the policeman who is 
directing him usually stand facing each other may have 

^ For further illustration, see Chap. X. 



MENTAL BACKGROUND 115 

something to do with the resulting confusion. The 
wayfarer's left is the policeman's right. This source 
of error is not absent from school. The drill-master 
and the sewing mistress standing in front of their class 
and trying to illustrate some motion run serious risk 
of confusion. They sometimes meet the difficulty by 
facing the same way as the class, and doing the best 
they can under the circumstances. The position is 
awkward for both pupils and teacher, but is found to 
be, on the whole, the best way out of an almost impossible 
situation. An alternative is to stand facing the class, 
and then give the demonstration with reversed arms; 
that is, the teacher uses the right arm when he wishes 
the pupil to use the left, and vice versa. This naturally 
requires special training on the part of the teacher. 



CHAPTER V 

Suggestion in Exposition 

We have seen that the process of influencing another 
mind acquires all the interest of a mystery, and the 
wonder of our being able to act upon the mind of an- 
other at all is increased when we discover that our own 
minds are far from being entirely at our own disposal. 
Psychologists are fond of pointing out that we cannot 
call up ideas at will; ^ that we are more or less at the 
mercy of chance recall; ^ that if ^^ activity seems to be 
self-caused change/' ^ then we have no such thing as 
mental activity; * that even the inventor has to wait for 

^ " Volition has no power of calling up images, but only of rejecting 
and selecting from those offered by spontaneous redintegration. But 
the rapidity with which the selection is made, owing to the familiar- 
ity of the ways in which spontaneous redintegration runs, gives the 
process of reasoning the appearance of evoking images that are fore- 
seen to be conformable to the purpose. There is no seeing them be- 
fore they are offered; there is no summoning them before they are 
seen." — Shadworth H. Hodgson : The Theory of Practice, Vol. I, p. 400. 

2 See the whole of the section on "Command of the Thoughts" in 
Professor Alexander Bain's The Emotions and the Will, pp. 369-382, 
particularly the famous passage (pp. 376-377) in which the mind is 
compared to a wild beast waiting to spring upon its prey, as soon 
as it appears, but quite unable to hasten that appearance. 

3 F. H. Bradley : Appearance and Reality, p. 64. 

^ G. F. Stout : Analytical Psychology, Vol. I, p. 155 : " It seems clear 
that if our whole conscious existence is so constantly and thoroughly 
dependent on factors extraneous to it, there is no room anywhere 
within it for purely immanent causality. It is impossible to find any 
bit of mental process which is determined purely from within." 

116 



SUGGESTION IN EXPOSITION 117 

some outside spark to touch off his loaded inteUigence.^ 
If we are distrustful of the evidence of the professional 
psychologists, we may turn to the evidence of the intel- 
ligent layman. The following is the view of a writer, 
not a professional philosopher, whose name is a house- 
hold word on both sides of the Atlantic. The passage 
occurs in a private letter to the author : — 

"A curious thing is the mind, certainly. It originates nothing, 
creates nothing, gathers all its materials from the outside, and 
weaves them into combinations automatically, and without any- 
body's help — and doesn't even invent the combinations itself, 
but draws the scheme from outside suggestion. . . . 

" It does seem a little pathetic to reflect that man's proudest pos- 
session — his mind — is a mere machine ; an automatic machine ; 
a machine which is so wholly independent of him that it will not 
take even a suggestion from him, let alone a command, unless it suits 
its humour ; that both command and suggestion, when offered, origi- 
nate, not on the premises, but must in all cases come from the outside ; 
that we can't make it stick to a subject (a sermon, for instance) if 
an outside suggestion of sharper interest moves it to desert ; that 
our pride in it must limit itself to ownership, ownership of a 
machine — a machine of which we are not a part, and over whose 
performances we have nothing that even resembles control or au- 
thority. It is very offensive. Any tramp that comes along may 
succeed in setting it in motion, but you can't. If you say to it : 
' Examine this solar system, or this Darwinian Theory, or this potato,' 
you can only say it or think it when the inspiration has come to you 
from outside. And to think that Shakespeare and Watt, and we 

^ F. Paulhan : Psychologie de V Invention, p. 10. Taking Newton as 
a typical case, Paulhan deals with the two essential elements, (1) the 
total results of Newton's previous thinking, and (2) the fall of the apple 
(or its equivalent) as the immediate cause of the discovery: "L'un 
indique la preparation lente de Tinvention, la tendance qui travaille 
a se completer, I'idee confuse cherchant 1' element qui la precisera; 
I'autre signale Toccasion venue, Telement nouveau qui se presente 
engage dans la perception (ou dans I'idee) d'oil I'esprit saura I'ab- 
straire, et determine la synthese nouvellC; la creation intellectuelle." 



118 EXPOSITION AND ILLUSTRATION IN TEACHING 

others can't even combine our idea-catches on plans original with 
ourselves, but that even the combination-scheme must come from 
the outside — gathered from reading and experience. 

" Meantime, which is I and which is my mind f are we two or are we 
one? However, it is not important, for if we say, 'I will think/ 
neither I nor the mind originated the suggestion — it came from 
outside." 

All this may be very depressing and even ''offensive" 
to the ordinary man. To the teacher it is full of en- 
couragement. For it must be remembered that in the 
process described he plays the part of the tramp. He 
does the stimulation from the outside. Archimedes 
prayed for a fulcrum for his lever, and promised that 
if his prayer were answered he would move the world. 
But as he could not step off the earth, the ttoO o-rw he 
desired remained an aspiration. The prayer that was 
refused to Archimedes in the physical world has in 
the mental been granted to the humblest teacher. So 
far from complaining that we are ''prisoned in sepa- 
rate consciousness'^ and cannot share the consciousness 
of our pupils, we ought to rejoice that we are enabled to 
stand outside the mind-world of our pupils, and from 
our vantage ground there move that world. To what 
extent we can move it is a different question. For 
here we come to an aspect of the matter that restores 
our self-respect as human beings, though it diminishes 
our power as teachers. The writer just quoted is un- 
duly depressed. It is true that the tramp can for the 
moment direct our attention this way or that at his 
will and against ours. But the amount of attention 
we give depends not on the tramp, but on the nature 
and content of the mind he seeks to manipulate. The 
power of the teacher, like the power of the tramp, is 



SUGGESTION IN EXPOSITION 119 

limited to directing the mind's attention. The deter- 
mination of the amount and the duration of the at- 
tention hes with the mind attacked. 

For the comfort of the teacher, and the discourage- 
ment of the tramp, it is well to remember that the time 
element is very important to the full understanding of 
this matter. The ordinary tramp can command im- 
mediate but only momentary attention to a particular 
topic. If he happens to know the sort of things we are 
interested in, and is able to talk intelligently about 
them, he no doubt is in a position to retain our atten- 
tion for quite a long while. But in doing so he ceases 
to form a part of mere external nature. He is no longer 
a mere tramp acting at haphazard. He is acting 
deliberately, and with a knowledge of what he is about. 
He is really usurping the teacher's place. Nor can we 
reasonably resent the exercise of the power he has over 
our minds. After all, it is we who have put this power 
into his hands. It is because we are what we are that 
he is able to manipulate us. To a certain extent he can 
make us act according to his will, but he can do this 
only by obeying the laws of our nature, by appealing 
to what he knows to be in us. He must adapt himself 
to us. He must respect our individuality. He must 
stoop to conquer. 

Having learnt the lesson of the tramp, it is now our 
business to discover what means we have at our dis- 
posal to manipulate effectively the mental content of 
another mind. Immediate recall in which an idea 
forces its way into consciousness by the mere strength 
of its accumulated presentative activity offers no 
difficulty, and mediate recall that takes the form of 
sense stimulation, as in the case of sights, smells, and 



120 EXPOSITION AND ILLUSTRATION IN TEACHING 

sounds reestablishing a whole that formerly existed, 
is almost equally free from trouble. But in the ordi- 
nary case in which one idea recalls a whole mass we 
have a notable complication. For an idea usually 
belongs to several groups. Certain ideas, it is true, 
are for most minds restricted to one definite mass. 
They have nothing whatever to do with any other mass. 
It is the function of technical terms to limit such ideas 
to their proper mass, and thus prevent confusion. The 
word ohm is, I believe, restricted to the science of elec- 
tricity, and for the ordinary person has no connection 
with any other group of ideas. Even here, however, 
I have no doubt that in the mind of a competent elec- 
trician the idea of ohm will have connections with sev- 
eral masses.^ 

Speaking generally, every idea forms a part of several 
masses. When an idea, then, obtains admission into the 
field of consciousness and proceeds to introduce others 
by mediate recall, the question arises: Of the various 
masses with which it is connected, which will it favour, 
which will it tend to reinstate ? 

At first sight the obvious answer is the strongest 
mass; that is, the mass that is richest in elements, is 
best arranged, and has the greatest accumulated pre- 
sentative activity. Reflection shows that if this were 
so, then in a given mind at a given stage the same idea 
must always call up the same mass. But experience 
proves that this is not the case. It has to be observed 

1 On making a testing, casual reference to the term in conversation 
with a distinguished physicist, Dr. WilKam Garnett, Educational 
Adviser to the London County Council, I found that in his mind it 
formed part of an historical mass, an economic mass, an educational 
mass, a laboratory mass, a workshop mass, a literary mass — at this 
point we were interrupted. 



SUGGESTION IN EXPOSITION 121 

that we are not here deaUng with the effect of the same 
idea on different minds. It is easy to guess the mass 
that a given idea will recall in the case of chosen types 
of men. The idea of vine will naturally recall his green- 
house to the retired merchant who is fond of garden- 
ing, to the hon vivant his favourite wine, to the devotee 
the fifth chapter of St. John, to the man home from 
Europe the slopes of the Rhine or of Burgundy, to the 
art-lover certain pictures and schools of painting, to 
the botanist some particularly long words. All this is 
plain sailing. But suppose we take the case of a man 
who combines the six conditions. It is surely not im- 
possible to find an old gentleman eager about his green- 
houses, fond of wines and pictures, an enthusiastic 
amateur in botany, full of memories of happy walking 
tours on the continent, and withal a constant church- 
goer and Bible-reader. He would be a rash man who, 
without knowing the old gentleman, would venture to 
predict which of the six masses the idea of vine would 
call up. Even if we made his acquaintance and dis- 
covered which masses had the greatest power in his 
consciousness, we would have only a slight probability 
in our favour in guessing the strongest mass as the one 
to be recalled. On the other hand, if we learn that the 
idea was brought before him while walking in his garden 
on an autumn evening when he had just become aware 
of the first appearance of frost for the year, we may 
with more confidence foretell the direction of his ideas. 
Yet even under these circumstances, if the old gentle- 
man had during the afternoon given instructions about 
heating the greenhouses, and so had his mind easy on 
the practical side, and if the friend with whom he was 
walking in the garden had been recaUing escapades 



122 EXPOSITION AND ILLUSTRATION IN TEACHING 

during their old Burgundy tramp, the chances are that 
the idea of vine would rouse the geographical and 
reminiscent mass. 

Before we can foretell the course of recall, we must 
know (1) the contents of the mind in question and 
the relative accumulated presentative activities of the 
masses; (2) the conditions under which the mediating 
idea is presented; (3) the actual contents of the con- 
sciousness immediately preceding the presentation. 

It is obvious that this is no mere theoretical problem. 
We are here dealing with the fundamental problem of 
Exposition. We desire a given mind to act in a given 
way. Our first step must be to learn the laws accord- 
ing to which it acts, and the conditions under which 
these operate. Having acquired this knowledge, we 
are able to interfere effectively with the course of 
thought in the mind of another. In ordinary life we 
are continually doing this, often quite unconsciously. 
Our every action in relation to others cannot but modify 
the course of thought in those others. Our very pres- 
ence often accomplishes such a modification without 
our even being aware of the existence of the person 
upon whose mind we have exercised an influence. For 
we have seen that we are all to a great extent at the 
mercy of external suggestion. 

In applying suggestion for our special purposes, then, 
the first consideration in presenting a new idea is 
to discover against which background it is likely to 
be projected. Apart from any special circumstances 
that may complicate individual cases, there are certain 
backgrounds that may be called the normals for cer- 
tain ideas. If this mark 1 3 be placed upon a black- 
board, we are entitled to assume that it will be projected 



SUGGESTION IN EXPOSITION 123 

against a background of numerals and read as thirteen. 
But if we place the word Ethel before it and the word 
Jones after it, we may be certain that it will be thrown 
against a literal background, and read as the initial 
of one of the names of a person. In nearly every case 
there is a preferential background against which an 
isolated idea will be normally projected. Naturally 
this varies according to the content of the individual 
mind. But examination will show that there is a gen- 
eral as well as a personal preferential background for 
each idea. It is useful for teachers to look into these 
preferences both personal and general. 

Take the case of homonyms. If the word one is 
uttered, most people who hear it will project it against 
a numerical background, though some will connect it 
with win. So with the word two : the numerical back- 
ground prevails, though in this case there are three 
homonyms to choose among. It is clear that it is not 
mere familiarity with the word that determines the 
choice here, for to occurs more frequently in ordinary 
reading and writing than does two. Speaking generally, 
a substantive meaning has the preference over a tran- 
sitive ^ meaning. I should have been inclined to make 
the statement without the reservation, had it not been 
for the results of certain experiments that I made to 
verify my general impression, which was based on 
ordinary observation. I selected five homonyms 
and pronounced the sounds ^ to various classes of pupils 
who were instructed to write down without hesitation 
the word that occurred to them. I have classified the 

1 See p. 43. 

2 The invariable sequence of the sounds, as dictated, was : one, he, 
rain, by, to. 



124 EXPOSITION AND ILLUSTRATION IN TEACHING 



results into three groups. Group I (representing the 
work of about 600 pupils) includes only pupils between 
9 and 10; Group II (about 2500 pupils) represents 
the work of pupils of ages varying from 11 to 15, 
the ages being pretty evenly distributed; Group III 
(close on 500 persons) gives the reactions of under- 
graduate students of ages ranging from 19 to 22 : — 



Homonyms 


Group I 


Group II 


Group III 




Percentage 


Percentage 


Percentage 


One . 
Won . 










99.1 
.9 


96.3 
3.7 


92.7 
7.3 


Be . 
Bee . 
Borb^ 










96.6 
3.4 


73.6 
26.4 


47.1 
40.0 
12.9 


Rain . 
Reign 
Rein . 










99.4 
.6 


76.8 

22.1 

1.1 


86.0 
11.2 

2.8 


By . 
Buy . 
Bye . 










96.6 
1.7 
1.7 


69.0 

25.1 

5.9 


52.7 

38.1 

9.2 


Two . 
To. . 
Too . 










3.7 

92.6 

3.7 


43.4 
43.4 
13.2 


77.2 
12.6 
10.2 


■r» J 




1 






1 '11 1 


Till ^• rr> 


1 / 



Practical teachers will have little difficulty in ac- 
counting for the differences in the various groups. 
The little children took the point of view of the dicta- 
tion lesson, and if they did happen to know any other 
form than the obvious one, preferred to stick to what 

^ Groups I and II had been warned that words were expected; 
this accounts for the absence of the mere letters in their case. 



SUGGESTION IN EXPOSITION 125 

they were quite sure of. The increase in the percent- 
age of less-known words is quite uniform as one moves 
up the school, and closely corresponds to the school 
standing of the pupils. With those who were quite 
free in their choice — that is, Group III — there is a 
steady preference for the substantive element ^ in 
every case but in that of By, It is this exceptional 
preference for a transitive element that made me 
qualify my general statement. There is nothing sur- 
prising in this preference for the substantive elements ; 
these form the natural resting-places of thought. 
Besides, the other words that do not carry a substantive 
element depend for their meaning on some relation, 
and relationship is discounted in this case by the fact 
that the sounds are by the conditions of the problem 
presented in isolation. Accordingly, non-substantive 
words are less likely to arise in the mind as compared 
with the words indicating substantive ideas, and on 
that account carrying an environment with them. 

In the case of homonyms both of which represent 
substantive elements, there is a preferential back- 
ground in favour of the more familiar. Thus, Rain 
clearly outstrips Reign, and that again Rein. We more 
naturally think of a containing vessel than of an eastern 
potentate when we hear the sound can (Khan). So 
with the word vessel that has just been used; when 
taken by itself, its natural background is the sea. 

On the other hand, with a given background we have 

^ As a matter of fact, I got a higher percentage of Bee's in a post- 
graduate class (average age twenty-three) than I did with any of the 
undergraduate classes ; but the numbers are too small (43 Bee's from 
a class of 70 students) to permit of our drawing any satisfactory con- 
clusion. 



126 EXPOSITION AND ILLUSTRATION IN TEACHING 

no hesitation at all in predicting the exact sense in 
which a given word will be accepted. The background, 
then, is of fundamental importance in suggestion. In- 
deed, suggestion often implies nothing more than the 
calling up of an appropriate background. The mind 
does the rest for itself. 

When we come to consider more exactly the nature 
of suggestion, we find the usual differences of opinion 
among psychologists. To begin with, we must keep 
clearly before our minds that we are concerned not with 
pathological cases but with normal, healthy people. 
There is a wholesome naturalness that is very attractive 
in the view supported by Mr. W. Macdougall,^ following 
G. Tarde, that suggestion may be regarded as a direct 
manifestation of the mode of behaviour called ^^imita- 
tion." But while many educational applications may 
be made on this basis, we are not much helped by it 
in the way of Exposition. There appears to be a very 
general agreement among psychologists that suggestion 
is ultimately based upon association, and it is probable 
that Mr. Macdougall's view is not inconsistent with the 
recognition of association as a necessary part of the 
development of suggestion. 

Wundt tells us that '^ suggestion is an association ac- 
companied by a concentration of consciousness on the 
representations engendered [angeregten] by the asso- 
ciation." ^ He limits the application of the term to 
''only those states of consciousness excited within us 
which are strong enough to resist — at least for the 

^ Social Psychology, p. 325. 

^ As I do not have the German text by me at the moment, I quote 
from Keller's French translation, Hypnotisme et Suggestion (Alcan), 
p. 72. 



SUGGESTION IN EXPOSITION 127 

moment — the contrary states of consciousness that 
tend to destroy them." When we come to educational 
applications of the term, we find that Professor P. Fehx 
Thomas prefers to define it as: ^'The inspiration of a 
belief, the true grounds for which escape us, which with 
greater or less force tends of itself to realise itself." ^ 
Thomas supports this view by a reference to J. M. 
Guyau's definition: ^Hhe introduction of a practical 
belief that of itself realises itself."^ Baldwin regards 
suggestion as ^Hhe tendency of a sensory or an ideal 
state to be followed by a motor state," ^ and quotes 
Janet's formula : ^'a motor reaction brought about 
by language or perception."^ This tendency towards 
realisation in action is very commonly implied in the 
use of the word suggestion; but surely it is not neces- 
sary to assume an impulse that issues in an overt act. 
We may surely suggest a line of thought as well as a 
line of action. If not, then suggestion is of very limited 
use to the mere expositor. Sometimes he desires his 
exposition to lead to a certain line of action, as we shall 
see in the chapter on the Story as Illustration. But 
it will frequently happen that he desires no more than 
mental activity. This, however, should satisfy the 
psychologists. It appears to satisfy Mr. Macdougall, 
who gives us: ^^ Suggestion is a process of communica- 
tion resulting in the acceptance with conviction of the 
communicated proposition in the absence of logically 
adequate grounds for its acceptance." ^ Later in the 



^ La Suggestion son Role dans V Education, p. 20. 

2 Education et Her Mite, p. 17. 

3 Mental Development in the Child and the Race, p. 105. 
* Aut. Psy., p. 218. 

^ Social Psychology, p. 97. 



128 EXPOSITION AND ILLUSTRATION IN TEACHING 

chapter we shall work up to a fuller description, but in 
the meantime it must be understood that by suggestion 
we mean the manipulation of the ideas of our pupil 
so as to produce a predetermined result, whether in 
thought or action. For success in our work we must 
depend upon the Wundtian concentration of conscious- 
ness on associations. 

The inspiration that leads to the concentration of con- 
sciousness may originate from within or from without. 
If it comes from within, we have what is commonly 
called auto-suggestion. It is sometimes questioned 
whether auto-suggestion is possible. The lay witness 
quoted on page 117 would certainly deny the possibility. 
For him suggestion necessarily comes from without. 
Professor Stout would at first sight seem to be on the 
same side, if we identify mental activity with the power 
of initiative. According to him, mental activity implies 
that mental process is determined purely by previous 
mental process.^ But even if we cannot produce a 
single '^bit of mental process that is determined purely 
from within,'' it does not follow that we have no power 
of initiation. We may never get rid of a certain resid- 
uum of stimulus from without, but all that this im- 
plies is that we are always kept in touch with the outer 
world, a condition that is in itself desirable. We may 
be able to remain open to all manner of external sug- 
gestion, and yet have the power to concentrate our con- 
sciousness in the manner Wundt demands; and this 
concentration may fairly be said to determine the suc- 
ceeding process in consciousness. Now according to 
Professor S. Alexander: ^^ What I have called mental 
activity is, in the usual language of psychology, cona- 

^ Analytical Psychology, Vol. I, p. 148. 



SUGGESTION IN EXPOSITION 129 

tion." ^ Auto-suggestion may therefore be said to 
occur when we will to concentrate our consciousness 
on certain associations. We know what those asso- 
ciations are, and we have a schematic knowledge of 
whither they are likely to lead. We may not be able 
to call up directly just the ideas we desire, but we can 
put ourselves in the most favourable situation to en- 
counter them. We can go where certain classes of 
ideas are to be found, and we may have the full as- 
surance that particular ideas, of which we are at the 
time of beginning our quest only vaguely conscious, 
will by and by sort themselves out and become focal. 
Probably pure auto-suggestion is a very rare phenome- 
non; but in any case it does not directly concern us 
here, for the suggestion that we are interested in is 
that which works from without, ^'foreign suggestion,'^ 
as it is called by Wundt and others. 

A certain confusion between auto-suggestion and 
foreign suggestion sometimes occurs through neglecting 
the point of incidence of the external influence. Some- 
times this is so far removed from the point at which 
suggestion begins to act that the subject has forgotten 
all about the external force (if, indeed, he ever observed 
it as such), and regards his action or thought as self- 
suggested. Some writers accordingly regard the term 
auto-suggestion with suspicion, and one ^ at least would 
like to use the descriptive term pseudo-auto-sugges- 
tion, were it not so intolerably cumbersome. 

A knowledge of the working of auto-suggestion may 
no doubt help the expositor in his preliminary examina- 
tion of the mental content of his pupils. A skilful 

^ Proceedings of the Aristotelian Society, 1908, p. 222. 
2 M. M. Keatinge, Suggestion in Education, 1907, p. 55. 



130 EXPOSITION AND ILLUSTRATION IN TEACHING 

observer like E. A. Poe's Dupin may be able to antici- 
pate the developments of a mental train self-origi- 
nated in another mind/ but as a matter of fact the ex- 
positor is almost entirely interested in trains of thought 
that he has himself originated. His interest is prac- 
tically confined to foreign suggestion, though it has to 
be remembered that the false auto-suggestion is in- 
cluded under this term. In fact, this false auto-sug- 
gestion is by far the most effective form. It greatly 
increases the power 6f suggestion, if what is really 
external suggestion should appear to the pupil to be 
auto-suggestion. The further back we can throw the 
incidence of the external influence the better the re- 
sults. Indeed, the root principle of the skilful use of 
suggestion is to make the mind of the pupil do as much 
of the work as possible. Why is it that suggestion is 
regarded as so much more dangerous in morals than 
direct statement or demonstration ? It is because sug- 
gestion merely starts a process; the mind carries it on, 
and in carrying it on is apt to think that it is acting 
on its own initiative. There is nothing so pleasant in 
mental process as self-activity,^ and if the mind can be 
made to feel that it is carrying out its own processes in 
its own way, it works with its maximum vigour. The 
further back the impulse from without can be thrown, 
the greater the chance of the pupil thinking that in a 
given case he is acting on his own initiative. ^^ Hus- 
band, voter, or pupil, they willingly follow a suggestion 

^ Though even here the ingenious Dupin really owes his success to 
his power of anticipating the effects on the given mind of the various 
external stimuli to which he observes it to be exposed. 

2 Compare Whately's explanation of the fact that the metaphor is 
more popular than the simile : " All men are more gratified at catching 
the resemblance for themselves than in having it pointed out to them." 



SUGGESTION IN EXPOSITION 131 

whose origin is so well concealed that it seems to be 
their own." ^ 

A pupil who can make no headway with a difficult 
rider in geometry may be helped by the teacher bluntly 
suggesting that the solution of the problem lies in the 
demonstration of the equality of two angles, CDE and 
RPQ, which, from their position on the drawing, do 
not seem to have any connection with each other, and 
certainly do not appear to be equal. But if the teacher, 
by shifting about the paper on which the drawing is 
made, is able to place it so that the equality of the 
angles is likely to strike the pupil's eye, he will set up 
a much more vigorous reaction than by merely stating 
the fact. The speaker who makes his conclusion fol- 
low immediately on the statement j of two premises 
saves time, no doubt, but does not have the same effect 
upon his hearers as the man who gives one premise 
at one time and the other a little later, and does not 
give the conclusion at all, but takes it for granted, 
and uses it in a further development of his theme. 
This is the method of the successful popular lecturer, 
and cannot be so usefully applied in the case of diffi- 
cult subjects presented to listless pupils. Even in 
such adverse circumstances, however, it will be found 
that an obvious inference is better left to the reluctant 
pupil. After all, he finds it less disagreeable to draw 
his own obvious conclusions than to have them thrust 
upon him from without. 

From what has gone before, it will be seen that there 
is nothing humiliating to the pupil in being thus ma- 
nipulated; for when all is said, the success of the 
manipulation depends entirely upon the nature and 

^ W. Mitchell, Structure and Growth of the Mind, p. 145. 



132 EXPOSITION AND ILLUSTRATION IN TEACHING 

content of the pupil-mind. If the pupil responds to the 
external stimulus, it is because the stimulus appeals to 
his nature. He responds to the stimulus because it 
has been so prepared as to respect his individuality. 
All the same there is a very natural objection to a 
system that may be in any sense described as ^'Educa- 
tion by deception.'^ Dr. Johnson is very angry with 
those who seek to manage other people in this way. 
Nobody likes to realise that he is managed by other 
people. It is true that Mr. Keatinge tells us in his 
book on Suggestion that ''Boys like to be managed," ^ 
but he certainly knows too much about boys to mean 
that they like to be managed in this insidious way. 
What he means is probably just the opposite. Boys 
like to feel that they are in the hands of a master, 
though this, again, is a little difficult to reconcile with 
the stress he lays upon the " contrariant " characters 
of the French psychologists. These characters are 
said to respond in the opposite sense to that sug- 
gested. In the case of rigid contrariants there is no 
difficulty, since all the suggester has to do is to change 
his suggestion from the positive to the negative, and 
the desired positive results will follow. With the 
more intelligent contrariants the attempt to use sug- 
gestion resolves itself into a trial of wits between the 
suggester and the subject, each trying to find out 
what the other really wants. It is because of the prev- 
alence of this contrariant spirit that the incidence of 
the external suggestion has to be so carefully watched. 
Dr. Sidis, in fact, goes the length of regarding the con- 
trariant attitude in our unhypnotised state as the nor- 
mal one, and enunciates the law of human stubborn- 

' p. 70. 



SUGGESTION IN EXPOSITION 133 

ness: ^^ Normal suggestibility varies as indirect sugges- 
tion, and inversely as direct suggestion.'^ ^ 

An important consideration for the teacher is that 
suggestion works in only one way. It is positive, not 
negative. By suggestion we may cause another person 
to think or act in a particular way; we cannot directly 
cause him not to think or act in a particular way. The 
power of the little word not is greatly overrated by some 
teachers. They are apt to think it is more efficacious 
to say, ''Don't use non with the imperative in Latin; 
use ne," than to say, ''With the Latin imperative, 
when we wish to signify negation, we always use ne.'^ 
What we wish to impress on the pupil's mind is that ne 
is the proper word to use under certain circumstances. 
Accordingly, we ought not to bring in the word non at 
all. With regard to conduct, the word not is very weak 
as a suggestion. In the early part of last century there 
was a town and gown riot in Aberdeen, and the students 
were not having the best of it. When they were driven 
within their own quadrangle, and had no available 
weapons the old principal, disappointed at this result, 
came out of his house, and shaking his fist at the stu- 
dents, shouted that they must not pull up the palings to 
use as clubs. Even had the old gentleman meant the 
negation seriously, it would have had no effect. There 
was only one suggestion in his remark, though there 
were two possible lines of conduct. 

Moral questions are not, however, urgent in the use 
to be made of suggestion in Exposition. Our interest is 
rather in the manipulation of ideas than in the particu- 
lar ideas to be manipulated. For our purpose it may 
be permitted to regard suggestion as a force applied 

^ Psychology of Suggestion, p. 89. 



134 EXPOSITION AND ILLUSTRATION IN TEACHING 

from without so as to bring into action organised 
powers latent in the mind of another, and by utihsing 
our knowledge of their organisation to cause these 
powers to act in a direction desired by the operator. 
A static result is not enough. If we bring under the 
notice of another person some of the elements of a back- 
ground that we know has previously existed in his 
mind, the likelihood is that this background will be 
thereupon reinstated. If this is all, we have an ex- 
ample of redintegration, and the process may not be 
recognised by some people as suggestion at all. It may 
be held that suggestion must lead to a definite line 
of mental activity^ and not to a mere reestablishment 
of a previous state. As a matter of fact, the redintegra- 
tion of a background materially affects the direction 
of the immediately succeeding activity. A reasonable 
description of the function of suggestion in Exposition 
is to say that it is the bringing of external influence 
(by means of words, signs, pictures, models, or what 
not) to bear upon a given mind so as to make it ap- 
perceive certain ideas in a way predetermined by the 
suggester. Since apperception is an active process, 
this description should meet the case. 

In teaching, as opposed to education, suggestion may 
be regarded as the process of initiating by more or less 
indirect means certain mental processes that have been 
so organised that when once begun they are carried 
out automatically. It may be said to be the tapping of 
the forces stored up by habit, the drawing of a cheque 
on the paid-up mental capital. We cannot suggest 
a process that has never before occurred in the mind. 
We fail just as we have failed when we have a cheque 
returned to us from the bank with the legend, ''No 



SUGGESTION IN EXPOSITION 135 

funds. '^ The crudest example of this class of didactic 
suggestion is to be found in the blunt giving of a few 
words that form part of the desired answer. Plain 
prompting is a kind of suggestion. Teachers some- 
times adopt a sort of disguised prompting that seems 
to give them satisfaction by saving them from the dis- 
grace of having to tell something that they feel in honour 
bound to elicit. The pupils in one case could not be 
persuaded to answer the question, ^^ Which English 
statesman was responsible for the loss of the American 
colonies?" The teacher encouraged them by telling 
them that they knew quite well if they would only 
think. They thought; but without success. At last 
the teacher had an inspiration, and asked, ^^What 
is the opposite of south?' ^ She was rewarded with the 
unanimous reply, ^'Lord North.'' ^ 

The teacher must not lose sight of the fact that, in 
addition to the deliberate and accidental suggestions 
of the moment, there are certain general lines of sug- 
gestion that work in a more permanent way. Most 
of these are what medical men would call benevolent, 
but some are malignant, and deserve special atten- 
tion. It is a desirable thing that when certain ideas 
are recalled there should at once arise by suggestion 
certain of the important elements implied in the con- 
notation of these ideas. But if only trivial elements 
are suggested, there arises the danger of a false concep- 
tion of the idea as a whole. The following extract from 

^ At a drawing-room meeting of a branch of the Parents' National 
Education Union, a very distinguished London physician maintained 
that he saw nothing wrong with this example of the use of suggestion. 
On the contrary, he believed it to be an excellent illustration, and a 
capital way of bringing the young people to the point. So hard is it 
to be efficient in two professions. 



136 EXPOSITION AND ILLUSTRATION IN TEACHING 

a clever novel ^ of journalistic and artistic life well 
illustrates this permanent suggestion of superficial ele- 
ments. The scene is a pubhshing office, and Mild- 
may, the art editor, is discussing with Martin, the 
literary editor, the illustrations submitted for an Egyp- 
tian story in a magazine. Martin begins : — 

"Where's the Sphinx?" 

*'Not mentioned in copy, '^ said Mildmay, moving a little farther 
behind Martin's chair. 

'* Where are the Pyramids ? " 

"The story contains no reference to the Pyramids," said Mildmay, 
quietly. 

"But — but — but — you know better than that, Mildmay ! " 
the editor protested, shocked and trembling. 

"But — but — my dear chap ! Here's a story about Egypt, and 
not so much as a Sphinx or a Pyramid or anything at all to suggest 
Egypt in it." 

"The chap who drew that, Martin, was on the Condor, and at 
Kassassin and Tel-el-Kebir." 

"Then he ought to know better than to send us a drawing like 
this:' 

An example of the most malignant form of the per- 
manent suggestion is to be found in the denominators 
of vulgar fractions. These have a peculiarity that is 
often disconcerting. They carry over to their frac- 
tional functions the associations of their integer con- 
nections, with the result that they suggest false 
estimates of the values of fractions. Some highly 
intelligent adults suffer from this permanent suggestio 
falsi. Most of us have come across men who believed 
that their club was more select than another, because 

^ Little Devil Doubt: by Oliver Onions, p. 290. 



SUGGESTION IN EXPOSITION 137 

it was necessary to have only a fifth of the balls 
black before rejection followed, while in the other club 
it required a tenth. 

Underlying the idea of percentage is the permanent 
suggestion of considerable numbers. Not infrequently 
illustrations in percentages convey a false impression 
on this account — not always unintentionally. Un- 
scrupulous persons quote the actual figures in all 
cases where they are large and imposing, and when they 
are unpleasantly small represent them by percentages. 
Grave injustice is sometimes done by the necessity 
of expressing certain official returns in uniform tables. 
A country teacher finds, for example, that her eighth 
grade is listed as having 100 per cent of failures in 
a certain examination. This reads like a complete 
breakdown of the school, whereas all that it means 
is the complete breakdown of dull John Brown, who 
happens to constitute the whole of the eighth grade for 
that year. Wherever the numbers concerned are very 
small, the permanent suggestion should be corrected 
by a statement of the actual figures. 

The following quatrain from Beranger's Les Gueux 
proved unexpectedly difficult in an examination in 
French : — 

"Vous qu'affiige la detresse, 
Croyez que plus d'un heros, 
Dans le Soulier qui le blesse, 
Peut regretter ses sabots." 

On investigation I found that the cause of the trouble 
was the force of the permanent suggestion of the word 
un. Though the students all knew, of course, that the 
word could mean one as well as a or an, the suggestion 



138 EXPOSITION AND ILLUSTRATION IN TEACHING 

of an article before a noun was so overpowering that 
most of the pupils had to make the best they could of the 
article-sense, and as a consequence they rang the varia- 
tions on ' ' more of a hero. ' ' A similar suggestion played 
havoc with a class called upon to read at sight a passage 
which they had not before seen from the Twelfth Book 
of the Mneid : — 

'' Ardentes oculorum orbes ad moenia torsit 
Turbidus, eque rotis magnam respexit ad urbem." 

Since the class had never encountered the enclitic que 
in this collocation with e, the horse-suggestion was over- 
mastering, supported as it was by the accompanying 
rotis. The majority of the pupils more or less in- 
geniously apostrophised a hypothetical horse. 

It sometimes occurs that relative terms acquire a 
permanent suggestiveness that leads to error. Towns 
on the east coast acquire a suggestion of easterliness. 
Most people, for example, who have not had their 
attention specially called to the matter, are under the 
impression that Edinburgh is farther east than Liver- 
pool, which does not happen to be true. It is difficult 
to believe that a place ^'west of the Andes" maybe 
''east of New York." The expositor must be continu- 
ally on his guard against these permanent suggestions. 

We have seen that the range of suggestion is limited 
to the mental content of the pupil. We can suggest to 
him new combinations of old elements of experience ; 
but we cannot suggest new experience. Further, we 
may be quite aware of the mental content of the pupil, 
and yet be unsuccessful in suggesting the proper ideas. 
We are familiar with the story of the American who in 
France did not know the word for mushrooms, but made 



SUGGESTION IN EXPOSITION 139 

a sketch of one, and had the mortification of being 
offered an umbrella. Palaeographers tell us that the 
early iconographs and ideographs are exceedingly sug- 
gestive. But when tested by application to modern 
pupils, it is not found that they make the proper 
suggestion. The accompanying two drawings are re- 




FlG. 1. 

productions of early Chinese iconographs. They are 
merely different ways of representing the same thing. 
But though the pupil has thus a double chance, it 
becomes clear on making the experiment with a class 
that none of the pupils can guess what the drawings 
ought to suggest. Yet the palaeographer tells us that 
this is regarded as ''an exceedingly clever abbreviation 
of a pictorial representation of flame." ^ The following 
are regarded also as particularly suggestive, but to 
English pupils, at any rate, they have proved quite 
unintelligible. 





WINDOW GARDEN CONSTELUATiON 

Fig. 2. 



Accompanied by the interpretation, all these icono- 
graphs are intelligible enough, and the symbolism is 

^ M. J. B. Silvestre: Paleographie Universelle. 



140 EXPOSITION AND ILLUSTRATION IN TEACHING 

quite apparent, but in themselves they suggest nothing. 
With the two following drawings as they stand 




V 



Fig. 3. 



I had no success whatever in eliciting the meaning 
from a class of intelligent students of average age 22. 
But when the help was given that they pictured male 
human beings who stood in a certain family relationship 
to one another, and that the silhouettes were taken from 
early Chinese writing, nearly half of the class were 
able to respond to the suggestion, and declared them 
to be father and son, the suppliant attitude of the son 
and the protecting attitude of the father being quite 
what one would expect, in view of what one hears of 
the filial relation in China. 

A similar difficulty in applying Suggestion is experi- 
enced in attempting to reproduce in graphic form certain 
states of mind. No doubt Sir Charles Bell ^ and others 
have succeeded in representing very faithfully some of 
the stronger emotions. But unobservant people fre- 
quently misunderstand excellent graphic presentations 
of human facial expression, and when we deal with less 
skilful presentations, even intelligent readers do not 
always respond successfully to the suggestions offered. 
M. Maurice Castellar, in illustrating the practical side of 
expression, gives nine photographs of persons whose at- 
titudes and facial expressions are supposed to indicate 

' Anatomy of Expression in Painting (1806). 



SUGGESTION IN EXPOSITION 141 

certain states of mind that are set forth in the explana- 
tory letterpress that accompanies them in his book/ 
There are in all seventeen individual figures, and in 
only four of these did an inteUigent class of students hit 
upon the state of mind that was described in the ex- 
planatory letterpress. Still, when the letterpress was 
read, the students were willing to admit that the photo- 
graphs might be said to represent quite well what was 
wanted. 

In the use of suggestion it is obviously of importance 
to discover the least possible amount of energy to be 
used to produce a given effect. We must seek out the 
minimum suggestible. It is sometimes discussed how 
much of a given complex must be presented before the 
whole is suggested to the mind. There can be no 
quantitative answer. We have no standard. Every- 
thing depends upon our familiarity with the complex 
in question. The case is sometimes put: How much 
of the stag must appear above the crest of the hill 
before the hunter is certain that he is dealing with a 
stag ? Clearly, it all depends on the hunter. There 
are some hunters who would require to see pretty nearly 
the whole animal before they would be certain, while 
others respond to suggestion at the first appearance of 
the tip of the antlers. 

With an object for which we are not prepared (the 
stag-hunter is assumed to have been waiting for a stag), 
we cannot say which element it is that suggests the 
complex. It does not come to us piecemeal, but as a 
whole. Going along a crowded street, we find ourselves 
thinking of a certain friend. Suddenly we become con- 
scious that there he is, a few steps in front of us. The 

* UArt de VOrateur: Paris, 1906. 



142 EXPOSITION AND ILLUSTRATION IN TEACHING 

thought of him has been suggested to us by the appeal 
of some of his physical qualities. If we are asked how 
we knew it was he from the mere appearance of his 
back, we find it difficult to say, and what we say, 
remember, is pure theory. The fact that it is we who 
have seen and recognised the man gives our evidence 
no more authority than that of anyone else; for the 
recognition was not made deliberately. Very probably 
the peculiarities that we select as distinguishing our 
friend had little to do with our recognition. We did 
not observe this thing and that, then reason out that it 
must be So-and-so; So-and-so sprang ready-made into 
our consciousness.^ 

The fact seems to be that if the different elements of 
a complex are firmly welded together, that complex can 
be suggested only as a whole. If we wish to recall to 
the mind of another the idea of a cow, we can do so by 
appealing to various senses, but so soon as the cow 
appears she appears as a whole; it is not a matter of 
one part appearing and being followed by another. 
Further, the cow that does appear is always the same 
cow for the same mind. We have all only one avail- 
able cow as idea. This idea may be aroused at any 
moment by the sight of the word cow, or by the pro- 
nunciation of that word, or by the lowing of some unseen 
animal, or by the peculiar odour that we associate with 
cowsheds, or by the sound of a peculiar kind of bell. 
However aroused, the resulting idea of cow in our mind 
is the same, if it be allowed to develop to its full extent. 
The preferred sense will no doubt have its effect in the 

* For an ingenious theory that does not agree with the above, see 
Dr. W. T. Harris's Psychologic Foundations of Education, Chaps. IX 
and X. 



SUGGESTION IN EXPOSITION 143 

setting in which the cow will be found, but the cow 
itself will be the same, however recalled. To be sure, 
this ideal cow is capable of improvement. Increasing 
experience of cows gives the idea greater content. But 
such a change is gradual. It remains true that for a 
given stage the available mental cow is constant for 
the individual. For suggestion this is the only cow. 
Changes can be effected only by supplying means of 
observation. 

The question is sometimes raised whether we are 
morally justified in using suggestion in such a way 
that the person operated on does not know that sug- 
gestion is being used. Note that stress is laid on 
the fact that the person affected is not aware that he is 
the subject of suggestion. But as a matter of fact, if 
the person knows that suggestion is being used, it is no 
longer a case of suggestion. If we openly advise a 
man to follow a particular line of conduct, we may be 
said in a certain sense to make suggestions. We may 
even put our advice in the very form of, ^^Well, I would 
suggest — " But this is quite a different process from 
that we have been considering in this chapter, — the 
problem of the sanction of suggestion solvitur ambu- 
lando. Whether we will or no, we are continually 
using suggestion in the sense in which we understand 
it here. It is true that we may use it sometimes more, 
sometimes less, deliberately. But even so, the problem 
has to be carried a step farther back before it is worth 
discussing. Not the use of suggestion, but the pre- 
paring the mind for suggestion, is the responsible 
work. Suggestion is powerless to do anything but set 
in motion forces that are latent but none the less ex- 
istent. The sight of means to do ill deeds makes ill 



144 EXPOSITION AND ILLUSTRATION IN TEACHING 

deeds done, only when the ill deeds are already within 
the mental content of the person tempted. Sugges- 
tion is powerful only in so far as it follows the laws and 
takes account of the content of the mind operated upon. 
This is the psychological explanation of the saying that 
to the pure all things are pure. No amount of sugges- 
tion can evoke from the mind ideas that are not there. 

Still, it cannot be denied that suggestion is capable 
of illegitimate applications. It is significant that the 
word is only now emerging from a very discreditable 
association in the dictionary, and even still the adjec- 
tive suggestive connotes a special and particularly 
vile class of things to be suggested. But the fact that 
the process is recognised as preeminently dangerous 
is only an argument the more for the educator seizing 
this specially powerful means of influencing his pupils. 
If it can so easily lead pupils wrong, it is surely our duty 
to learn how to use it on the side of right. There is 
no reason why evil should monopohse suggestion. 

From the moral standpoint, the purpose of education 
is really to make the pupil suggestible to certain in- 
fluences. The good boy is the boy who responds to 
suggestion in the way that his teacher regards as right. 
In intellectual instruction the same may be said. The 
boy who knows a subject really well is the boy who can 
be depended upon to respond loyally to suggestion in 
his subjects. Suggestion, while a valuable means of 
Exposition, is also in itself one of the goals of intellec- 
tual education. 



CHAPTER VI 

Conditions of Pkesentation 

Peesentation is one of the Five Formal Steps that 
are now the common property of all who deal with 
method in teaching. 

The very name Formal Steps implies two underlying 
assumptions. It takes for granted, in the first place, that 
it is possible to separate form from matter in teaching. 
One may be a little surprised to find in these steps that 
originated with Herbart this emphasis on the formal 
side. The usual criticism against him and his followers 
is that they attach undue importance to the nature of 
the matter to be presented to the pupil. According 
to them a man is what he is because he knows what 
he knows. When we find, then, that the Herbartians 
commit themselves to form at all, we may take it for 
certain that the matter to be taught is not neglected. 
The Formal Steps are a statement of the process of 
teaching, with the minimum reference to the nature of 
the matter to be taught. We can never entirely elimi- 
nate consideration of the subject-matter of instruction, 
but in the formal steps it is maintained that the separa- 
tion of form and matter has been carried to the ulti- 
mate point. By following these steps it is claimed that 
the teacher will best guide the pupil in the process of 
learning, and that with the minimum consideration of 
the nature of the matter to be learned. 

L 145 



146 EXPOSITION AND ILLUSTRATION IN TEACHING 

The second assumption is that instruction should 
proceed by definite steps. Comenius warns us with 
some energy, and not a httle repetition, that nature 
never proceeds by leaps, but always by steps. Herbart 
has taken this warning to heart, and has systematised 
the steps in teaching that he believes nature would have 
us follow. We must not confound the need for step- 
wise progression with the speed with which progress 
is accomplished. Whatever nature may do, children 
certainly sometimes appear to proceed by leaps in their 
thinking. We often accuse them of jumping to con- 
clusions. But this does not show that they have not 
proceeded stepwise, unless by stepwise we mean that 
every step must be deliberately taken. The fact that 
I go upstairs three steps at a time does not prove that 
I am not going upstairs. I proceed stepwise, though I 
take big steps, and though I do not take every indi- 
vidual step that I might. The clever pupil may pass 
over many steps that the teacher may feel called upon 
to deal with in class, and the stupid pupil frequently 
requires additional steps to be interpolated between 
what may be regarded as the normal steps; but both 
kinds of pupils are proceeding along in the same direc- 
tion, covering the same course, though the one has to 
touch the ground much more frequently than does the 
other. The number of steps to be taken is one ques- 
tion, — and in itself a very important one, particularly 
in relation to class-work, — the order in which these 
steps have to be taken is another. It is mainly with 
the order of the steps that Herbart deals when he 
speaks of the Formal Steps. 

As a matter of fact. Presentation does not occur among 
the steps originally suggested by Herbart. These were 



CONDITIONS OF PRESENTATION 147 

only four, named respectively, Clearness, Association, 
System, Method.^ These names are not very suitable 
as descriptions of processes, so later writers have in- 
troduced certain changes. The first step, that which 
leads to clearness in the pupil's mind, is really made up 
of two processes, and may therefore be regarded as a 
double step. The first of these processes consists of 
analysis: the contents of the pupil's mind must be 
analysed so that he may be prepared to receive the new 
matter. The second consists in a synthesis of the new 
matter with the old. The analytic step has been named 
preparation, and the synthetic, presentation. It may 
not be amiss here to emphasise the fact that prepara- 
tion in this sense means preparation of the pupil's mind, 
not the teacher's. There has been a good deal of dis- 
cussion about the naming of the different steps. Prob- 
ably the most widely accepted nomenclature of the 
five steps now generally recognised is. Preparation, 
Presentation, Association, Generalisation, and Applica- 
tion.^ 

It is sometimes held that in the first two steps we are 
working on the perceptual plane. Certain elements of 
our past experience have been combined with certain 
new elements; but that is all. The new wholes thus 
formed are yet mere units, though they are in them- 
selves complex. They must now be brought into rela- 
tion with other wholes. At this stage we are not very 
particular which other simple or complex units they 
are brought into relation with. What we want is to 

^ Allgemeine Pddagogik, Book II, Chap. 2. 

^ For a tabular presentation of the various classifications of the 
Steps by the followers of Herbart, see p. 139 of Charles de Garmo's 
Herbart in the Great Educators Series. 



148 EXPOSITION AND ILLUSTRATION IN TEACHING 

bring the new unit into relation with as many other 
units as we have at our disposal. To bring this about, 
the best means is easy discussion, not in the sense of 
argument, but rather in that of free conversation. The 
teacher can work up the association of a subject in 
different ways. He may suggest as many similar ideas 
as he can, and thus encourage comparison, with a view 
to bringing out resemblances. Or he may call up as 
many contrary ideas as the experience of his pupils sup- 
plies, and thus lead to arrest by force of contrast within 
the same field. Or he may change the point of view 
from which the newly presented ideas are to be viewed, 
and thus show them up against different backgrounds. 
The purpose of this third formal step — called Associa- 
tion — is to find the true place of the new combination 
in the nature of things as represented by the present 
content of the mind in question. The associations 
formed at this stage may be of a purely accidental 
character. Naturally most of the ideas with which 
the newly acquired elements are compared or contrasted 
have something in common. But in turning over ideas 
in the mind, combinations of purely disparate ideas must 
frequently be formed. The complexes thus formed 
are at this stage not of primary consequence, though 
they should all be able to bear the test of comparison 
with an objective standard. What is at present aimed 
at is the familiarising of the new elements with their 
surroundings in the mind. 

The next step, called Generalisation, goes further. 
Like association it implies the grouping together of the 
elements of experience, but this time the grouping is no 
longer a matter of chance or arbitrary choice. We 
have to advance from mere grouping to system. 



CONDITIONS OF PRESENTATION 149 

Association supplies us with the materials for forming 
concepts, but it is the work of the Generahsation 
step to develop the concept. This is why the step 
is variously named System, Concentration, and Gener- 
alisation. Underlying each of the elements joined to- 
gether at the step of Association, there is a deeper 
meaning than appears at the first casual glance. At 
the associational stage we regard this chair and that as 
self-existing objects. They are no doubt related to 
other objects inasmuch as they all coexist in time and 
space. But the essential oneness of all chairs is really 
perceived at quite an early stage. The child behaves 
intelligently towards a chair that he has not seen before 
if he has already had dealings with a few chairs, or even 
with only one if the new chair is not too unlike the first. 
But he does not realise this oneness till he has had it 
brought to consciousness by a process of generalisation. 
The process of generalisation is apparently a very 
complicated one, and when we reflect that it implies as 
a necessary preliminary the process of abstraction, we 
seem to have ruled it out of court altogether so far as 
young pupils are concerned. But as a matter of fact 
it is not necessary to go through the complete process 
of philosophical generalisation in the junior school- 
room. Without, of course, knowing of the existence of 
such a thing as the self-conscious level, the very young- 
est pupils generalise with ease. It is indeed the fatal 
ease with which they generalise that calls for such care- 
ful treatment. It is not the difficulty in getting them 
to generalise that need concern the teacher, but the 
difficulty of preventing them from generahsing wildly. 
Children begin to generalise in their nurse's arms. 
When a child calls a cat a bow-wow, or a dog a pussy, 



150 EXPOSITION AND ILLUSTRATION IN TEACHING 

we say he generalises rashly. As a matter of fact he is 
guilty of an undistributed middle. But the appeal to 
reason at this stage is out of the question. Not rea- 
soning is wanted, but experience. 

To avoid rash generalisations the association step 
must be carefully made. Ordinary experience secures 
that in the great majority of cases the association step 
is sufficiently elaborated to prevent at least such rash 
generalisations as are dangerous. In actual teaching 
the association step can be so manipulated as to meet 
the special needs of the generalisation about to be made 
in the next step. For instance, if the teacher is afraid 
that the pupils are likely to fall into Sir Thomas 
Browne's rash generalisation and maintain that no 
quadruped lays eggs, the conversation at the associa- 
tion stage may be directed to frogs, crocodiles, and such 
troublesome exceptions to an otherwise unobjectionable 
generalisation. The value of the conversational method 
lies in the fact that it turns attention in a great variety 
of directions, and thus brings forward collocations of 
facts that produce healthy contradictions, and prevent 
generalisations that otherwise might have passed mus- 
ter. The greater the knowledge the teacher possesses 
of the content of the minds of his pupils, the more 
effectively can he direct the course of the association 
step. But even with the best-informed teacher there 
must always remain a vast unexplored region of the 
pupil-mind which can be best dealt with by the free 
course of conversation. 

Once the generalisation has been obtained, there is 
room for ingenuity in the way of fixing it in the memory 
of the pupils. The apt phrase, the epigrammatic 
definition, the broad general rule are all here in place. 



CONDITIONS OF PRESENTATION 151 

Even the moral, if well expressed, may have its claims 
recognised on the condition that it has been worked 
for by the pupil. When once the moral has been 
worked for and expressed in the pupil's blundering 
language, there can be no harm in translating his halt- 
ing sentences into crisp English. 

The final step is named Application. We must not 
rest content with imparting facts, correlating them 
with facts already known, and deducing from them the 
underlying meaning. They remain as mental lumber 
till they are applied in actual life. It is one thing to 
know: it is quite another to be able to use knowledge. 
A very useful classification of our pupils may be made 
on this point. There are those who have much more 
knowledge than they can make use of, and those who 
could make use of much more knowledge if they had it. 
We are familiar in school, and perhaps more familiar 
still in ordinary life, with the person that can make a 
little knowledge go a very long way, and also with the 
person that is full of knowledge and cannot make any 
use of it. A good method of Exposition must do some- 
thing towards bringing these two extremes together. 
The earlier of the formal steps provide the knowledge 
in the best form : the final step sees that this knowledge 
gets a field on which it can be exercised. 

It is quite possible for the pupil to have a piece of 
knowledge without being at all able to use it. In 
several hundred classes I have held up a six-inch foun- 
tain pen and invited the pupils to tell me how long 
a half of three-quarters of it was. I had but a small 
percentage of answers. Yet the moment the prob- 
lem was stated on the blackboard as ^^Find the value 
of one-half of three-fourths of six inches, '' most of the 



152 EXPOSITION AND ILLUSTRATION IN TEACHING 

pupils were indignant at being asked such an easy one.^ 
This final step, then, is the place for exercises of all 
kinds. Till the pupil has applied his knowledge in some 
way, it is not really knowledge to him. It is something 
inert, dead, useless. When the application step has 
been completed, the knowledge is living; fact has been 
turned into faculty. This may not unfitly be described 
as the aim of the whole series of formal steps. They 
have served their purpose if they have so presented and 
manipulated the facts that they have become faculty. 

Two common lines of error in the application of 
these Formal Steps have done much to diminish their 
usefulness. 

In the first place there is a tendency among the more 
matter-of-fact teachers, those who are just a little above 
the rule of thumb, to emphasise unduly the second step. 
To such ultra-practical teachers Presentation is the 
only step that need be seriously considered. It is the 
one bright gleam of light in an otherwise dark system. 
To present new ideas to the pupil's mind : that is teach- 
ing. All the other steps are more or less pedantic 
refinements, but Presentation is something real, some- 
thing that commends itself to a man of common sense. 
Yet as a matter of fact complete Presentation is pos- 
sible only in so far as all the other steps are taken. It 
may seem trifling to say that the mind can accept only 
what it has been prepared for; but the constant neglect 
of this commonplace is the cause of much unsuccessful 
teaching. The practical teacher is right in seizing 
upon Presentation as being the most important of 

^ As illustrating the power of the mere form of expression, it is 
interesting to note that I got somewhat better results when I asked 
for o?2e-half than I did when I asked for a half. 



CONDITIONS OF PRESENTATION 153 

the five. It may not unreasonably be maintained 
that the whole five steps are only different aspects of 
Presentation in its wide sense. But we must not con- 
fuse a special aspect of Presentation separated off from 
the others and labelled the second step, with Presenta- 
tion as a name for the whole process that cannot be 
completed without the whole five steps. 

The view that all teaching resolves itself into the 
direct giving of information, the telling the pupil 
something new, has produced a natural reaction which 
leads to error in the application of presentation, or 
rather by the elimination of presentation. From 
their studies in theory young teachers are inclined to 
avoid anything in the form of direct presentation. 
The second step, while still monopolising their atten- 
tion, is regarded with suspicion. What is contemp- 
tuously called ^' telling'^ is regarded by these young 
teachers as in the highest degree unintelligent and un- 
scientific, and they fall into ludicrous errors in their 
efforts to avoid it. Everything must be, in the words 
of their text-books, ^^ elicited from the pupil by skilful 
questioning. '^ They do not realise that there are two 
kinds of knowledge: one that must be communicated 
directly, and another that may be worked up from 
materials already in the mind. We want very badly 
a couple of words to keep these two kinds of know- 
ledge from getting mixed. I cast covetous eyes on the 
two words information and instruction. The first 
would very well represent the communication of new 
facts, the second might stand for the rearrangement of 
facts that are already known to the pupil-mind in one 
way, but that by being recombined may produce 
knowledge that was latent, if you like, but that certainly 



154 EXPOSITION AND ILLUSTRATION IN TEACHING 

would never have come to light at that stage, but for 
the intermediation of the teacher. It is information 
to tell me the Japanese word for a tree. If I do not 
happen to know the word, no amount of skilful 
questioning will ever elicit it from me. On the other 
hand the generalised formulae of Euler^s Theorem ^ 
may be said to be implicit in the pupiPs mind before 
he approaches the problem. All the teacher has to do 
is to arrange that certain ideas shall be grouped in a 
particular way, and the formulae issue of themselves. 
The meaning of instruere, that our dealings with Caesar 
have familiarised us with, comes in very appositely 
here. The general draws up the line of battle, now 
making one formation, now another. In every case 
the men, like the ideas, are given. Information is as 
different from Instruction as recruiting is from drilling. 
The second error in the application of the Formal 
Steps is just the opposite of what we have been consider- 
ing. Instead of being tempted to overestimate one of 
the Steps and neglect the others, the teacher may be 
impelled to insist too rigidly on the individual rights 
of each step ; in other words, to insist pedantically on the 
Steps, the whole of the Steps, and nothing but the Steps. 
For long, students in the training colleges of Great Brit- 
ain arranged their Notes of Lessons in three columns, 
at the top of which stood the words Heads, Matter, 
Method, respectively. The Formal Steps came along 
and introduced a welcome elasticity into the form of 
note-making. Unfortunately the new system is rapidly 
settling down into the old rigidity. The student first 
of all makes the mistake that every lesson must exem- 
plify the whole of the Steps, forgetting that the teaching 

* See p. 34. 



CONDITIONS OF PRESENTATION 155 

unit does not necessarily coincide with the lesson unit. 
It may take several lessons to complete the cycle of 
the Steps in respect of some important section of a 
subject. Besides, all the Steps are not always of the 
same importance. Particularly the two steps, Associa- 
tion and Generalisation, have very different values 
according to circumstances. It is no uncommon ex- 
perience to find a student coming to her Mistress of 
Method with the distressing news that she ^^ simply 
can't get a generalisation for this lesson." As a matter 
of fact, the one important thing is that a subject should 
be so presented that when the lesson is over the new 
matter shall have been worked into the very warp 
and woof of the mental content of the pupils. In the 
process the Formal Steps give very useful guidance, but 
that guidance must be of a general kind. Application, 
for example, need not be kept entirely to the end of the 
process. Frequently it comes in very appositely along 
with Association. Sometimes generalisation may force 
itself in before association has had time to complete 
its work, and sometimes there may be no need of gener- 
alisation at all. The Steps meet the case of the normal 
mind under normal conditions, but they have been 
formed on experience of how the mind acts, and are not 
something above the mind, and therefore something 
that the mind must obey. Most people who have had 
to do with the training of teachers have had experience 
of the complaint expressed to a class that is answering 
ahead of what the teacher's notes arranged for: ^'But 
you don't know that yetJ^ This means that the 
pupils have anticipated what, according to the teacher's 
calculations, is not due for several questions yet. In 
such cases it may still be desirable, for the sake of the 



156 EXPOSITION AND ILLUSTRATION IN TEACHING 

duller members of the class, that the teacher should 
insist on going through what he had intended. But 
he must realise that there is no absolutely fixed rate 
at which pupils learn. 

All the same, it is not a matter of indifference in what 
order facts are presented to the pupils. Old facts that 
have to be recalled, and new facts that have to be pre- 
sented, cannot be put forward haphazard. It may 
be impossible to lay down any fixed law according to 
which presentation must always be made, for some- 
times one fact and sometimes another may be the best 
to bring forward first. Everything depends upon the 
mental content of the pupil, and the purpose the teacher 
has in view at the time. It is conceivable that the 
same matter might have to be presented by the teacher 
in quite a different order to the same class, according 
as the lesson is to be given at the beginning, the middle, 
or the end of a given session. Indeed, so important is 
this question of order, that as soon as we have dealt 
with some other of the conditions of presentation, we 
shall devote a couple of chapters to it. 

One of the most popular problems in examination 
papers for teachers is to work out the relation between 
the inductive and the deductive methods of teaching. 
The orthodox answer seems to be that we should begin 
with the inductive, and end with the deductive. But 
obviously the two methods cannot be dissociated in a 
wholesale way. No doubt in dealing with a particular 
part of a subject one method or the other has the prefer- 
ence, but when we view the field of school work as a 
whole, we find that there is a place for both, all through 
the pupil's course. Speaking generally, new matter is 
acquired by inductive methods and applied by deduc- 



CONDITIONS OF PRESENTATION 157 

tive. But in the application by means of deductive 
methods we put ourselves in the way of learning at 
least some new matter as well as establishing what we 
have already mastered. It is not that we are inductive 
at the beginnings of our subjects and deductive later 
on. The two processes interlace even at the beginning. 
Some law must be laid down, some datum given even at 
the start. Thus in making a beginning of the teaching 
of Latin, we may either give a few rules of construction 
and a few Latin words with their meanings, and set our 
pupils to read a bit of Latin; or we may give our 
pupils a bit of Latin and tell them its general meaning, 
then set them to find out the meaning of the individ- 
ual words and to learn the meaning of case, number, 
person, and what not, from their experience of the way 
in which words behave in Latin passages. The first 
method would be generally described as deductive, the 
second as inductive.^ Obviously there are inductive 
and deductive elements in both. The alternation 
between the two methods characterises the whole 
course by which the boy acquires a mastery over his 
subject. 

This alternation of the different methods is paralleled 
by a different form of rhythm that is characteristic of 
Exposition. This is the alternation between the con- 
centration beat and the diffusion beat. Viewed from 
the standpoint of psychology, this is usually regarded 
as the rhythm of attention. But it is not a matter 
merely of greater and less attention, but rather a change 
in the area of the field within which attention is dis- 
tributed. There is a tendency among teachers to 

^ For the Inductive Method in Latin teaching, see Bennett and 
Bristol's The Teaching of Latin and Greek, p. 80 ff. 



158 EXPOSITION AND ILLUSTRATION IN TEACHING 

confound intensity of attention with the narrowness 
of the range within which it is exercised. A pupil 
may attend as intently to a wide field that he has 
under observation as he does in concentrating his atten- 
tion on the tip of a blade of grass in that field. In 
practice it is found that there is need for continual 
change of what may be called the focus of attention, and 
of this changing focus the expositor must take careful 
heed. Microscopic work affords us a useful parallel. 
The observer usually begins by using the low power, 
say 70, to get a general idea of the specimen under 
examination. By and by he wants to get a more 
detailed view of some part. Accordingly he uses a 
higher power and turns on perhaps the 350 objective. 
Some part of the new field he desires to examine in 
still further detail, and in consequence he uses the 700 
objective. But while working with these high powers, 
he begins to get a distorted view of the object as a 
whole, and to correct this he returns to the lowest power 
of all. It is because of this need for continual change 
from one power to another that the double nozzle and 
the multiple nozzle are supplied to microscopes, so 
that with the minimum outlay of time the field of 
vision may be changed according to the degree of detail 
the observer desires. 

In Exposition we are continually changing our focus, 
and there is a certain danger that the expositor's focus 
may change without a corresponding change on the 
part of the pupil. The Expositor may be working with 
the 700 objective while the pupil is working with the 
70. The tendency in Exposition as in microscopic work 
is to use the higher powers too freely, or rather too 
frequently, without reference to the low powers. It 



CONDITIONS OF PRESENTATION 159 

is natural to suppose that the higher the power, the 
more the pupil will learn. There is the misleading 
'^permanent suggestion'' ^ of the word thorough. To 
know a thing thoroughly is generally understood to 
mean to know it in great detail. But it is not unusual 
to find a person who knows a subject in great detail 
and yet has no command over that subject, because 
he has not correlated the details to the broad general 
principles. In Exposition the teacher must concentrate 
now on this point, now on that ; but he must never fail 
to correlate the minute points of the concentration beat 
with the broad outlines of the diffusion beat. He must 
learn from the painter who goes close up to his canvas 
to peer into it and put in a delicate stroke or two only 
to step back a few paces so as to get the general effect. 
The painter is attending as keenly at the long range as 
he is at the short one, and doing quite as valuable 
work. 

It is obviously of the first importance that expositor 
and pupil should be at each moment working with the 
same power. This is sometimes secured by the ex- 
positor making use of certain conventional expressions, 
such as '^speaking very generally," ^Haking a wider 
view we find," '^coming now to details we see." Apart 
from specific verbal cautions, the best way to maintain 
identity of power is to use the material in such a way 
as to lead to difficulties if it is presented along with 
material that belongs to a different grade. This may 
be best illustrated by the case of history, where we have 
the possibility of a geographical background. Besides, 
we are able, by the kind of characters we introduce, to 
indicate the general scope of our Exposition. We may 

» See p. 136. 



160 EXPOSITION AND ILLUSTRATION IN TEACHING 

have half a dozen historical manuals all of the same size, 
yet dealing with widely different fields of history. We 
may have one dealing with Ancient History, another 
with The History of the United States; a third may 
be An Epitome of the History of the World, while a 
fourth is The History of Partney Parish. We have 
here four quite different powers, and while a certain 
number of events are common to two or more of the 
volumes, the importance of those events is entirely 
different in the various volumes. The Renaissance 
might be treated in four different powers at different 
times, with the same advanced class. Under the 70 
objective we might treat of the great movement that 
north of the Alps culminated in the Reformation and 
on the south of the Alps in Humanism. The 200 
objective would give scope for a lesson on the state- 
ment that '' Modern History begins with the reign of 
Henry VII.'' Under the 500 objective there would 
be enough detail to work out The Effect of the Renais- 
sance on the Public Schools of England. ^^The 
Renaissance is epitomised in Erasmus" would be a 
theme that could be satisfactorily treated only under 
the 1000-power object-glass. 

This sliding scale of focus emphasises the relativity 
of everything that can be said on the subject of Expo- 
sition. There is a natural desire for a standard of 
some sort to which different cases may be referred. 
The ordinary thermometer with its two fixed points 
of departure — the freezing and boiling points of water 
— rouses our envy and challenges competition. In 
attempting to set up two points as a basis of comparison 
in Exposition it must be remembered that we are work- 
ing on the subjective side, and that therefore the points 



CONDITIONS OF PRESENTATION 161 

will vary with each individual treated. It is com- 
paratively easy to standardise the expositandum, the 
matter of Exposition, but so soon as we enter upon the 
subjective consideration of that matter we must be 
prepared for difficulties; we must face the problem of 
the individual mind. 

It is possible to obtain two points that are fixed for 
any given individual at a given time. They change in 
the course of the pupil's development, and they do 
not coincide exactly in the case of different pupils at 
approximately the same stage of development. But 
they are fairly definite within the experience of the in- 
dividual, and the coincidence with corresponding points 
in pupils of the same standing is sufficiently close to 
give the points a certain practical value. 

The first may be called the Inference Point. It 
marks the stage in any given subject at which the pupil 
has to go through a process of inference, however slight. 
Up to this point everything in that subject that is 
presented to the pupil is accepted at its face value. 
If on glancing at the sky a man remarks, ^^I see it is 
going to be a fine day to-morrow, '' he is dealing with a 
matter that is below his Inference Point. No doubt 
he is really making an inference and not merely record- 
ing an observation. He does not see that it is going to 
be a fine day, but from what he sees he infers that the 
day is going to be fine. So closely related, however, 
are the facts observed and the deduction drawn from 
them, that the whole process is practically one. When 
a number of facts and deductions from facts are so 
welded together as to become independent organised 
groups, the mind requires merely to observe them 
in order to accept them as wholes without criticism. 

M 



162 EXPOSITION AND ILLUSTRATION IN TEACHING 

Wherever this happens, the mind in question is working 
below its Inference Point. But when the Inference 
Point has been reached, it is necessary to do conscious 
work. Ideas have to be compared and correlated, 
and deliberate deductions drawn from previous expe- 
rience. A medical student at a clinical examination is 
working well above his Inference Point. The case 
may be an easy one, but the student is quite aware of 
the processes by which he reaches his conclusions. 
A mere glance at the patient tells the examiner all that 
it is necessary to know. The few perceptual impres- 
sions that act on the examiner's mind call up at once 
certain groups of ideas with which they have become 
in his mind so closely associated as to form one whole 
which represents the disease from which the patient is 
suffering. Obviously the Inference Point in a given 
subject which the student is studying is continually 
rising. What he has to reason out painfully at the 
earlier stages becomes a part of his being. As soon as a 
fact becomes faculty, it falls below the Inference Point. 
With growing experience fact after fact takes its place 
in complexes that remain below this point. The num- 
ber of groups of ideas that may be accepted at their face 
value is always increasing. 

Botanists tell us that at the tip of each twig there is 
what they call '' the growing point." The plant as a 
whole increases by the multiplication of cells according 
to their special fashions, by budding, fission, gemmation, 
or what not. But in whatever way the}^ multiply they 
always produce cells of exactly the same kind. Sap 
cells produce sap cells and no other kind, bast cells 
other bast cells, wood cells other wood cells, and so on 
all round — except at the growing point. There the 



CONDITIONS OF PRESENTATION 163 

cells are undifferentiated and multiply so as to produce 
cells that are fitted to become at need sap cells, or cam- 
bium cells, or bast cells, or whatever other kind the plant 
stands specially in need of at the time. The range 
above the Inference Point corresponds to the growing 
point of the plant, is indeed the growing point of the 
mind. It is in this region that the nurture of the mind 
takes place. 

It would seem as if there could be no limit to the 
region within which inference, conscious inference, is 
exercised. But there is an upper limit to the region 
of Inference when the matter is considered from the 
point of view of teaching and learning. The Infer- 
ence Point marks the limit of paid-up mental capital. 
All the matter that lies below it may be called upon at 
a moment^s notice, with the full assurance that it will 
come at once and behave as it is expected to behave. 
It is organised almost to the automatic level. Above 
the Inference Point the matter on which the mind acts 
is still organised, though the organisation is less com- 
plete. In certain directions the organisation is more 
and more to seek, and a stage finally comes at which 
the subject cannot be said to be organised at all. When 
this stage has been reached in a given subject, we may 
be said to have attained the Gaping Point. It indi- 
cates the limit of organisation of the mental content. 
Up to this point everything is dealt with under definite 
categories. The mind is prepared to manipulate the 
matter in certain definite ways : it puts certain standard 
questions and knows how to deal with the answers. 
If, however, some matter is presented that the mind 
does not know at all how to deal with, the Gaping Point 
has been reached. All that the mind can do is to turn 



164 EXPOSITION AND ILLUSTRATION IN TEACHING 

over this new matter in various ways, look at it from 
this point and from that; in fact, gape at it. 

A mineralogist has a new substance presented to him 
for examination. It is not sufficiently characteristic 
to be at once classified by inspection. Accordingly 
it rises above the Inference Point. He proceeds to 
apply this test and that according to his system. 
He observes its colour, its crystalline form, and its gen- 
eral texture. He strikes it with his hammer to hear 
how it rings. He breaks off a piece to discover its 
fracture. He pounds a small portion to get the colour 
of the powder. He tests its hardness compared with 
his standard minerals. Then he goes to his laboratory 
and discovers its specific gravity, its chemical compo- 
sition, its reaction to heat, electricity, and other things. 
All this while he has kept on asking certain definite 
questions. He knows exactly the sort of information 
he wants. His examination has been guided by pre- 
vious experience, and therefore admits of experiment. 
If now, in consequence of his investigations, he finds 
that not only does the result not fit into any system of 
classification with which he is acquainted, but that 
several of his individual results contradict each other, 
he has come very near the Gaping Point. It remains 
for him to consult his books and his friends. If as the 
result he finds that the mineral remains a mystery, he 
has actually reached the Gaping Point; for not only 
does he not understand the mineral, but he does not 
know how to go about discovering its meaning. 

Everyone who has had experience in working riders 
in geometry has had experience of the Gaping Point. 
At first we treat the problem in certain definite ways 
dictated by previous experience. This proposition 



CONDITIONS OF PRESENTATION 165 

and that will be applied. But if after a time every- 
thing we know has been applied in vain, all that can 
be done is to gape at the problem, and wonder whether 
anything will turn up to suggest new lines of investi- 
gation. We look at our drawing upside down, side- 
ways, obliquely, any way that may enable us to surprise 
the hidden meaning; just as we do in that typical case 
when we are reduced to the Gaping Point by the very 
bad handwriting of a friend. 

Like the Inference Point the Gaping Point is not 
stationary. After many illegible letters from our 
friend we begin to know that certain tiny scratches 
mean the; that a particular wriggle always means ing, 
another wriggle ation, and a third ly; that what looks 
like e is always a; and that of is always omitted. Out 
of this we form a system by means of which we can pro- 
ceed scientifically to deal with the body of the letter, 
though probably at the end there will be a small por- 
tion still left at the Gaping Point. 

But if it is important to remember that our Inference 
and Gaping Points are continually changing, it is much 
more important to realise that our pupils' Points are 
quite different from ours. What is below the teacher's 
Inference Point is often at the pupils' Gaping Point. 
No better way of testing a teacher's skill in manipulat- 
ing the two Points could be found than an examination 
of the use he makes of the word therefore. With mat- 
ter below the Inference Point of his pupils the teacher 
is entitled to bring his therefores closely together, but in 
subjects within the pupils' Inference zone the teacher 
should see that a good deal of matter is placed between 
each therefore. We have all met the brilliant mathe- 
matician who puts down one line of algebraic symbols 



166 EXPOSITION AND ILLUSTRATION IN TEACHING 

on the board, immediately followed by another, the 
only bridge from the one to the other being this ag- 
gravating word. Sometimes it takes pages of close 
^ ^ figuring ouf before a pupil contrives to bridge the 
gulf that his teacher has dismissed with a therefore. 



CHAPTER VII 
Beginnings in Exposition 

Accepting the view that Exposition consists essen- 
tially in producing among the elements of the mental 
content of the pupil a combination that coincides with 
the combination existing in the mind of the teacher, 
it is obvious that there must be a double process of 
analysis before a beginning can be made. First the 
teacher must review his own mental content so as to 
discover which elements are of importance for the pres- 
ent purpose. Naturally all the necessary ideas can- 
not be called up at once; but all the salient elements 
will readily come into consciousness and the presenta- 
tive activity of all the other relevant ideas will be 
quickened by the presence in consciousness of those 
that have actually risen above the threshold. The 
subconsciousness is filled with ideas bearing upon the 
subject. The mental content of the teacher is there- 
fore in a favourable condition for entering upon the 
work of Exposition. 

Next we have an analysis, as far as this is possible, 
of the pupil's mental content in relation to the matter 
about to be presented to him. This process obviously 
corresponds to the beginning of the Preparation Step, 
dealt with in our last chapter. Before we can prepare 
the mind of the pupil we must discover which parts of 
its content are relevant to the subject in hand. The 

167 



168 EXPOSITION AND ILLUSTRATION IN TEACHING 

regular teacher of a class has obviously a great advan- 
tage in this particular. From his previous dealings with 
the pupils he has a very effective knowledge of the ideas 
which he can rely upon finding at their disposal. With 
a new subject, or an entirely new branch of an old sub- 
ject, there is a certain danger of fogginess about the 
available mental content. But even under such cir- 
cumstances the class teacher need seldom wander far 
afield in order to find connecting ideas. A teacher with 
an entirely new class has, of course, to feel his way by 
questions and careful observation of the effects of what- 
ever presentations he ventures to make. 

With a fairly distinct knowledge of the ideas to be 
conveyed to the minds of the pupils and the com- 
plexes to be formed in those minds, and a less clear but 
still adequate knowledge of the ideas and complexes 
at present existing in the minds of the pupils, the teacher 
is prepared to enter upon the next stage, which consists 
in comparing the pupil mental content with the teacher 
mental content, and selecting a starting-point for the 
exposition. It will be found that the two mental con- 
tents overlap each other to some extent. There may 
be a larger or a smaller common segment, but in every 
case where Exposition is possible there must be some 
elements common to the two contents. If no common 
element can be found. Exposition is out of the question. 
Very frequently with a new or difficult subject the 
teacher has to cast about for a little before he finds the 
overlap that is necessary to secure a starting-point. 
Sometimes, on the other hand, the two mental contents 
coincide. In other words the pupils have all the ele- 
ments necessary for the full understanding of the 
matter in hand, though these elements may be at pres- 



BEGINNINGS IN EXPOSITION 169 

ent SO arranged as to give a different result from that 
desired by the teacher. The complexes in the pupil- 
mind may be all wrong as tested by an objective stand- 
ard; as, for example, in the first two stages of Herbert 
Spencer's progress towards a true theory of the colour 
of shadows/ In such cases the teacher's business is 
to break up the false complex by Confrontation and 
replace it by a better. But it sometimes happens that 
the pupil's complex is true so far as it goes, or true in 
certain connections, and yet there are other com- 
plexes to be made that are equally true, or that are 
true in a wider sense. In cases of this kind it is not 
necessary to break up the first complex. It may be 
temporarily analysed in order to separate out the ele- 
ments so that they may be built up into the new com- 
plex that for some reason or other the teacher regards 
as necessary for the pupil. But there is no need to 
introduce dispeace into the original combination of 
ideas; it may quite well coexist along with the new 
one, as a permanent part of the pupil-content, though 
the elements of which it is composed may now be cap- 
able of forming a totally different whole when required. 
For example, the complex ^^ primary colours" is made 
up of the elements red, blue, and yellow. But while 
this is found to be a true collocation so far as pigments 
and their manipulation are concerned, it is unsatisfac- 
tory when colours are treated from the standpoint of 
psychology. What are primary colours from the one 
point of view are not primary from the other. But 
the pupil who has had the psychological primary colours 
— red, violet, and green ^ — firmly grouped together 

' See p. 76. 

2 Cf. A Primer of Art, by the Hon. John Collier, p. 44. 



170 EXPOSITION AND ILLUSTRATION IN TEACHING 

as the result of later exposition, need not dispense with 
his old pigment combination of red, blue, and yellow. 
Both complexes are useful, each in its place. As a 
matter of fact, for the ordinary needs of life, we have to 
adopt still a third complex, for we have even psycho- 
logical authority for the statement that: ^'The pri- 
mary colours for the mind are the four principal colours 
— red, yellow, green, and blue.^' ^ When we begin to 
study chemistry and form new combinations of ideas, 
these need not in any way interfere with our old com- 
binations as represented by such familiar phrases as 
'^acid drops,'' or '^ table salt." The chemist may call 
these ^ trivial or irregular names,'' ^ but they represent 
wholes that are as real as those represented by his 
systematic terms. The rainbow complexes found in 
Genesis and in lyrical poetry need not be broken up 
because we have formed new combinations under the 
heading ^'ihe refraction of light." 

It is seldom that the teacher needs to use up every 
individual element in a given complex in order to build 
up another complex. The much more common case 
is that there has to be a general analysis of the pupil- 
content in order to get the elements necessary to build 
up a desired complex. In the process, it frequently 
occurs that certain elements necessary for our new com- 
plex are found to be lacking, and must be supplied by 
the teacher before any progress can be looked for. 
In any case the beginning must be made in that part 
that is common to the pupil-content and the teacher- 
content. Frequently there are many possible starting- 
points within the common area, and the selection must 

^ Lightner Witmer : Analytical Psychology, p. 181. 

^ Dr. Edward Frankland : Lecture Notes for Chemical Students, p. 11. 



BEGINNINGS IN EXPOSITION 171 

be determined by the purpose the teacher has in view, 
and the Hne he intends to follow. 

While it is admitted that the teacher must, at the 
beginning of his exposition, know definitely what his 
purpose is, it does not necessarily follow that this pur- 
pose need be communicated to the pupil. As a matter 
of fact at present serious consideration is given to this 
problem among the German teachers. There is much 
that is of interest in the discussions that centre in what 
they call the Zielangabe ; that is, the giving or state- 
ment of the purpose of the lesson at the very start. 
The term is usually closely associated with the name 
of Tusikon Ziller,^ though his critics spend a good deal 
of time in proving that the idea of stating clearly at 
the beginning of a lesson the purpose of that lesson is 
none of his invention,^ and is in fact of very venerable 
antiquity. The text of a sermon, the title of a book, 
the heading of a chapter are referred to as familiar ex- 
amples of the Zielangabe in ordinary life. But such 
cases do not always supply a parallel. Frequently 
the text and the title are used to whet curiosity rather 
than to indicate purpose. Indeed the misleadingness 
of titles is a cause of increasing complaint among 
readers. When the student of elocution punctiliously 
begins his recitation with '^Barbara Frietchie, a poem: 
by John Greenleaf Whittier," his introduction can 
hardly be classed as an example of the Zielangabe, 

^ See his AUgemeine Padagogik, dritte Auflage, p. 162 ff. 

^ While there is httle difficulty in finding examples of the applica- 
tion of the principle of the Zielangabe, it is not so easy to give cases 
in which it is deliberately applied as an educational principle. As 
far back as 1780, however, we find E. Ch. Trapp using in his Versuch 
einer Padagogik (p. 315) the term Zielsetzung, which he uses in quite 
the Zillerian sense. This reference I found in Karl Richter. 



172 EXPOSITION AND ILLUSTRATION IN TEACHING 

But when in our peculiar idiom a lecturer tells us that 
he '^proposes'' to do certain things in the hour at his 
disposal, we have a genuine Zielangabe. 

The very fact that writers on Education have thought 
it worth while to use the word as a technical term, and 
to discuss its exact meaning and function, marks it 
out as indicating a noteworthy stage in the develop- 
ment of the theory of presentation. It indicates among 
other things the more or less conscious adoption of the 
heuristic attitude in opposition to the Socratic, as most 
suitable for the teacher to take up. By the very fact 
of recognising the necessity for the pupil to know the 
object of the lesson, the teacher proclaims that he ex- 
pects his cooperation; in other words, the activity of 
the pupil is assumed. He is not merely to be supplied 
with facts and conclusions; he is to be made to work 
out conclusions for himself. The goal of the lesson is 
set before him as something to be attained; the means 
of attaining it are not specifically indicated. A great 
part of the value of the lesson would be lost if this were 
not so. Misapplications of the heuristic method supply 
illustrations of the abuse of the Zielangabe. ^'To dis- 
cover the chemical composition of water ^' is a legiti- 
mate Ziel or aim to set before a class ; but when 
we find in a pupil's note book that the matter is put: 
^'To find the chemical composition of H2O," we realise 
that something has gone wrong. On the other hand: 
^'To prove that water is composed of Oxygen and Hy- 
drogen'' is quite a legitimate Ziel. 

It is clear that the Zielangabe cannot be limited to the 
lesson-unit. It would be inconsistent to maintain that 
the pupil must know definitely the purpose of each 
lesson, and yet be kept in ignorance of the purpose of 



BEGINNINGS IN EXPOSITION 173 

each part of the lesson. One Ziel is not enough to guide 
throughout a whole lesson. There must be many inter- 
aims, or as Campe calls them, Zwischenziele} But if 
there are to be inter-aims, there must be inter-units. 
We must have our matter cut up into sections, at the 
beginning of each of which must appear an inter-aim 
or Zwischenziel. Each of these sections must be com- 
plete in itself, the completeness being determined in 
relation to purpose. They need not by any means be 
of the same length; the one condition is that they must 
be little wholes.^ 

Sometimes the Zielangahe becomes a mere matter of 
pedagogic routine, and exercises no real influence on the 
lesson. This is specially true of lessons that form part 
of a course. Here the whole matter dealt with by the 
teacher is so closely connected together that it is some- 
times neither possible nor desirable to cut it up even 
into lesson-lengths, not to speak of smaller sections. 
The general amount of work to be done at each class 
meeting must, of course, be determined, but it does not 
follow that the whole need be separated into purpose 
units of uniform magnitude. The purpose of one les- 
son has frequently to be carried over into the next. 
Accordingly, we find that sometimes the German teacher 
who is loyal to the theory of the Zielangahe finds him- 

^ " Soil die Jugend auf demselben nicht ermiiden, so muss man ihn 
durch viele Zwischenziele verktirzen und angenehm machen. Auch 
ohne Riicksicht auf Erieichterung fiir die Jugend hat dieses Zielsetzen 
einen grossen Nutzen." (Campe: Allgemeine Revision des gesammten 
Schul- und Erziehungswesens, 8 Teil, 1787, S., 180 ff.) Quoted by- 
Karl Richter. 

2 Amongst certain "long-known rules of teaching" Diesterweg in- 
cludes "Lass das Kind kleine Ganze auffassen; gieb ihm kleine 
Ganze." 



174 EXPOSITION AND ILLUSTRATION IN TEACHING 

self forced to begin with the ludicrously attenuated 
Ziel: ''Our object in to-day ^s lesson is to see what hap- 
pens next/' ^ What leads to this absurdity is the 
notion that the Zielangdbe is a sort of pedagogic rite 
to be gone through at the beginning of each lesson- 
period. The theory of the Zielangahe does not demand 
that the time-unit and the purpose-unit must be iden- 
tical. The essential point is that the pupil should know 
whither he is going, so that he may cooperate with the 
teacher, and do his fair share of the work.^ 

It is true that there may be occasions when it is 
not only unnecessary but unprofitable for the pupil 
to be told the exact purpose of a lesson. In many 
lessons given on the Socratic Method, for example, 
the very essence of the teaching is the unexpectedness 
with which certain conclusions are reached. It is 
well that the pupil should not know that the purpose 

^ " Ja nach einer Bemerkung in den ' Erlauterungen zum Jahrbuche 
von 1883/ die also nach Zillers Tode erschienen sind, hat Ziller spa- 
ter selber stillschweigend zugelassen, dass das Thema z. B. fiir eine 
Geschichtsstunde auch so formuliert werden konne: 'Wir wollen 
sehen, wie es weiter geht.'" Karl Richter: Die Herbart Zillerschen 
Formalen Stufen, p. 131. 

2 " Nicht nur der Lehrer muss wissen, was er in dieser Stunde er- 
reichen will, sondern auch die Schiller sollen es wissen, dass ein be- 
stimmtes Ziel gesteckt ist, iiber das sie am Schlusse der Stunde 
miissen Rechenschaft geben konnen. Dadurch wird der Gedanken- 
gang konzentriert, es wird das Gefiihl der Erwartung und Spannung, 
die Lust und Freude zur Losung der gestellten Aufgabe erregt. Fehlt 
Jenes Ziel, so wird der Schiller wie ein Blinder mit verbundenen Augen 
vom Lehrer gefilhrt, und eine eigene Willensanstrengung ist un- 
moglich. Die Schiller miissen am Schlusse der Stunde eine bestimrate 
Antwort auf die Frage geben konnen : Was habt ihr heute gelernt ? 
Wovon habe ich gesprochen ? Schlimm ist es wenn sie keine Ant- 
wort geben konnen, oder vielleicht sagen : Wir haben allerlei gehabt." 
Ferdinand Leutz : Lehrbuch der Erziehung und des Unterrichts, 4 Au- 
flage, Zweiter Teil, p. 40. 



BEGINNINGS IN EXPOSITION 175 

of the lesson is to make him aware of certain gaps in 
his knowledge. In the Socratic Method the pupil is 
working towards two ends: one that he knows he is 
working towards, and one that is known only to the 
teacher. It does not follow that pupil and teacher are 
working at cross purposes. We are deahng here with 
the educational effects, and these are best produced 
without the pupil's conscious cooperation. His coopera 
tion is, of course, essential, but the teacher loses his 
position of advantage as an external influence if he 
explains to the pupil the educational effect to be pro- 
duced, and urges him to assist in being educated. 

Even in matters of mere knowledge it may sometimes 
be an advantage to omit a statement of the Ziel. It 
is largely a matter of the distribution of interest. 
When the Ziel is given, the interest Hes in the means 
of attaining it; when it is withheld, the interest lies 
in the process itself, particularly in relation to the 
suspense as to what it is going to lead up to. This 
contrast between the place of the Zielangahe in the 
Heuristic and the Socratic Method will, if carefully 
investigated, lead to the conclusion that the real dif- 
ference lies in the magnitude of the purpose unit. 
No teacher would suggest that his pupils should be 
kept entirely in the dark with regard to the purpose of 
the work he is engaged in. The question always is: 
How wide an outlook is it advisable to offer them? 
With advanced pupils ^ we can give much wider aims 
than those that apply to each lesson as it comes round. 
It is probable that teachers are too easily content with 

^ Campe tells us: "So wie die Jugend heranwachst, kann man 
die Hauptziele nach Monaten, Viertel-und halben Jahren stecken." 
Allgemeine Revision as above. 



176 EXPOSITION AND ILLUSTRATION IN TEACHING 

the mere Zwischenziele : it is certain that the pupils 
are. So long as the pupil is allowed to go on dealing 
with each step as an independent unit, he is usually 
quite content to work away without looking for any 
wider or deeper meaning. Pisgah views are not to his 
liking, and he will certainly not climb the mountain 
unless under pressure, or at least under encourage- 
ment. One of the redeeming features of school ex- 
aminations is that they bring into occasional promi- 
nence the main aims (Hauptziele), that give meaning 
to the Zwischenziele with which the pupil is too apt to 
be content. 

Teachers of arithmetic are now laying great stress on 
the need for clearly imaged ends in the minds of the 
pupils before beginning to work out problems. The 
pupil must not be left merely to multiply and divide 
in the hope that somehow the answer will come out. 
The following extract gives a graphic account of a state 
of mind that is too common in our schools. It is 
taken from a school story called The Rickerton Medaly 
which is the work of a practical teacher. The scene is a 
a class room in an elementary school. Mr. Leckie, the 
teacher of the class (Standard VI, average age about 
13), propounds a problem in arithmetic: — 

" If 7 and 2 make 10, what will 12 and 6 make ? " 

A look of dismay passed over the seventy-odd faces as this 
apparently meaningless question was read. Everybody knew that 
7 and 2 didn't make 10, so that was nonsense. But even if it had 
been sense, what was the use of it ? For everybody knew that 12 
and 6 make 18 — nobody needed the help of 7 and 2 to find that out. 
Nobody knew exactly how to treat this strange problem. 

Fat John Thomson from the foot of the class raised his hand, 
and when asked what he wanted, said : — 

" Please, sir, what rule is it ? " 



BEGINNINGS IN EXPOSITION 177 

Mr. Leckie smiled as he answered : — 

"You must find out for yourself, John; what rule do you think 
it is, now ? " 

But John had nothing to say to such foohshness. "What's the 
the use of giving a fellow a count ^ and not telling him the rule ? " — 
that's what John thought. But as it was a heinous sin in Standard 
VI to have "nothing on your slate," John proceeded to put down 
various figures and dots, and then went on. to divide and multiply 
them time about. 

He first multiplied 7 by 2 and got 14. Then, dividing by 10, 
he got If. But he didn't like the look of this. He hated fractions. 
Besides, he knew from bitter experience that whenever he had frac- 
tions in his answer he was wrong. 

So he multiphed 14 by 10 this time, and got 140, which certainly 
looked much better, and caused less trouble. 

He thought that 12 ought to come out of 140; they both looked 
nice, easy, good-natured numbers. But when he found that the 
answer was 11 and 8 over, he knew that he had not yet hit upon the 
right tack; for remainders are just as fatal in answers as fractions. 
At least, that was John's experience. 

Accordingly, he rubbed out this false move into division, and 
fell back upon multiphcation. When he had multiplied 140 by 12, 
he found the answer 1680, which seemed to him a fine, big, sensible 
sort of answer. 

Then he began to wonder whether division was going to work this 
time. As he proceeded to divide by 6, his eyes gleamed with tri- 
umph. 

"Six into 48, 8 an' nothin' over, — 2-8-0 an' no remainder. 
I've got it ! " 

Here poor John fell back in his seat, folded his arms, and waited 
patiently till his less fortunate fellows had finished. 



James ^ knew from the "if" at the beginning of the question that 
it must be proportion ; and since there were five terms, it must be 

^ Scotice : any kind of arithmetical exercise in school work. 
' The clever boy of the class. 

N 



178 EXPOSITION AND ILLUSTRATION IN TEACHING 

compound proportion. That was all plain enough, so he started, 
following his rule. 

" If 7 gives 10, what wiU 2 give ? — less." 

Then he put down 

7 :2: :10: 

"Then if 12 gives 10, what will 6 give? — again less." So he 
put down this time 

12:6 

Then he went on loyally to follow his rule: multiplied all the 
second and third terms together, and duly divided by the product of 
the first two terms. This gave the very unpromising answer If. 

He did not at all see how 12 and 6 could make If. But that 
wasn't his lookout. Let the rule see to that. 

The problem of beginning is often complicated by 
the fact that it is not recognised as a problem. It 
seems so easy. There are so many possible beginnings 
that it would appear that one could hardly fail to hit 
upon something that will exactly meet the case. Some 
teachers, in fact, deliberately minimise the importance 
of the beginning. Too much time is spent over con- 
siderations of beginning, they maintain, and advise 
their pupils to get to work anyhow. The important 
thing, they say, is to get a start. It does not matter 
how you begin, so long as you get begun. There is 
perhaps a certain justification for all this impatience. 
An experienced editor, in engaging a brilliant young 
man to assist him in preparing for the press manu- 
scripts that had been accepted for his magazine, gave 
this advice: ''In many cases, particularly with essays, 
you will find it a good plan to cut out the first paragraph. 
The author gets down to business in the second. 
You will, of course, be prepared to have all the authors 
complain that the first paragraph is the best in the 
essay, the fact being that they have given so much time 



BEGINNINGS IN EXPOSITION 179 

and care to the beginning that they have lost all sense 
of its true value." What the editor objected to here is 
not so much beginnings as ^^introductions.'' No one is 
more tired of formal openings than the experienced 
trainer of teachers. He of all men is fully convinced 
that introductions are excellent things to omit. But 
the lesson must be begun all the same, and the problem 
of the beginning remains. 

It may not be a logically justifiable statement that 
there are many degrees of beginning, but it contains a 
definite meaning. We have indeed the whole range from 
the beginning of an entirely new subject to the begin- 
ning of a new sentence. There is a certain rhythm in 
teaching, and each new beat in this rhythm implies a 
new beginning. Obviously, the longer the beat the more 
important the beginning. It is, however, only at the 
bigger divisions of a subject that any serious prob- 
lem arises. At the subordinate divisions the begin- 
ning is practically determined by what has gone before. 
In dealing with a subject, the teacher acquires a swing 
that carries him on over all the smaller breaks in con- 
tinuity. A lesson in the middle of a course has to a 
certain extent determined its own beginning with regard 
at least to matter, and often with regard to form as well, 
inasmuch as the reaction between teacher and pupil 
throughout the course has led to the development 
of the teacher- and pupil-content in such a way as to 
estabhsh a more or less inevitable interaction between 
them. But the very beginning of a new subject, 
and especially when the teacher is new to his class, 
presents a very different problem. It involves the 
breaking in somewhere or other into the pupils' circle 
of thought, and it is often of material consequence 



180 EXPOSITION AND ILLUSTRATION IN TEACHING 

where this irruption takes place. The subject-matter 
may be approached from many different points, and 
nothing but a fair knowledge of the pupils' mental 
content can determine which it is best to select. 

That this difficulty in beginning is not an imaginary 
one originating in an excess of refinement in method is 
proved by the trouble often experienced in ordinary 
life when we set about explaining anything that is in the 
least complicated. We often toss about for a while, 
seeking the most suitable starting-point. Sometimes, 
indeed, we actually put our difficulty into words, and 
ask: ''Well, now, where shall I begin?" And it is to be 
noticed that we do this even in what we are apt to 
regard as the simplest case, that is, in the telling of a 
story. When a Frenchman does not follow a confused 
story as it is being told to him, he is apt to say to the 
story-teller: '' Si tu voulois commencer par le commence- 
ment." The reference is to Anthony Hamilton,^ the 
brilliant Irish writer of French fairy tales. In one 
of Hamilton's stories Moulineau the giant calls upon 
the ram (who, of course, is one of the speaking kind) 
to cheer him up by telling some pleasant tale : — 

" The ram, after having meditated for a little, began in this way : — 

'After the wounds of the white fox, the Queen had not failed to 
pay him a visit.' 

'Ram, my friend/ said the giant, interrupting him, 'I understand 
nothing of all that. If you would begin at the beginning, you would 
give me pleasure ; for all those tales that begin in the middle only 
confuse the imagination.' 

'Very well,' said the ram; 'I consent, against the custom, to 
put everything in its place ; accordingly the beginning of my story 
[histoire] will stand at the head of my narrative [recit].' " 

' Died 1720. 



BEGINNINGS IN EXPOSITION 181 

Here Moulineau takes it for granted that it is a self- 
evident proposition that we should always begin at 
what he calls the beginning. No doubt there are 
intellects for which this rectilineal arrangement is the 
best possible. Moulineau would have been at home 
in China, where, we are told, the drama begins with the 
birth of the hero, and goes straight on. Even in Eng- 
land there is room for the orthographic story of the 
Robinson Crusoe type: — 

"I was born in the year 1632, in the city of York, of a good 
family, though not of that country, my father being a foreigner of 
Bremen, who settled first at Hull . . .," etc. 

but there is also a place for the Iliad, Paradise Lost, and 
the modern complicated novel that begins in the middle 
of the plot. Yet Moulineau is right in insisting upon 
beginning at the beginning : his mistake lies in suppos- 
ing that chronology is the only element that determines 
what a beginning is. Time is, of course, of fundamental 
importance in thinking, but it must not be allowed 
to dominate the expositor in his selection of material. 
He must be guided in every case by the purpose he has 
in view. In dealing with Moulineau it is clear that the 
proper order is chronological; in dealing with a jaded 
pubhc, tired of the ordinary and in search of excitement, 
the ram's successors are entitled to neglect the chrono- 
logical order, and to adopt the chronological middle 
or end for their purposive beginning. The expositor 
wishes to produce a certain arrangement of ideas in the 
mind of another: the beginning that lends itself best 
to the production of this arrangement is the best. 

The teacher in an English school begins, for instance, 
with a blackboard full of figures from the Board of 



182 EXPOSITION AND ILLUSTRATION IN TEACHING 

Trade returns for the past ten years, from which the 
pupils are invited to discover which are Britain^s 
best customers in the matter of buying her goods. 
Various ups and downs are noticed, and causes sug- 
gested. One sudden fall is unaccounted for. Tow- 
ards the end of 1906 Italy began to buy a good deal 
less from Britain. The fall is not temporary, for there 
has been no corresponding rise since. Italy is not 
hostile to Britain: rather the contrary. The cause 
must be sought elsewhere. More figures are sub- 
mitted, from which it appears that what Britain has 
lost Germany has gained. But why this sudden change ? 
Germany is no nearer Italy than it was before; there 
has been no quarrel with British goods; the Germans 
may be better at pushing goods, but there was no 
sudden increase in their superiority at that time. 
Gradually the search is narrowed down to something 
peculiar that belonged to that year, and the opening 
of the Simplon Tunnel in May, 1906, is suggested. 
Since this beginning occurs in a lesson in commercial 
geography, the tunnel is approached from the proper 
point. Moulineau would have insisted upon start- 
ing with the tunnel. 

A problem of this kind is often an excellent way of 
beginning an exposition. Instead of starting straight- 
way with the subject of the difference between the 
development of the Feudal System in England and in 
France, the problem might be suggested : Why are there 
hedgerows in England and not in France ? In answer- 
ing this interesting question all the essential points of 
difference emerge, and the incentive of a well-defined 
purpose is maintained throughout the lesson. 

The problem of beginning is important not merely 



BEGINNINGS IN EXPOSITION 183 

because of its relation to the interest aroused, but also 
because it practically fixes the order in which the 
lesson must afterwards proceed. In a lesson on the 
development of the butterfly, we may begin with 
the egg, or with the imago, with the grub, or with 
the chrysalis. If we begin with the egg, we would 
satisfy Moulineau, and follow the development up- 
wards. If we begin with the imago, we follow the 
development backwards. In both cases we have no 
break in the time series. If, now, the start is made 
with either of the intermediate states, there must be a 
double progress, one part forwards, the other back- 
wards. At first sight it would appear that there is 
only one way of beginning this exposition properly. 
The egg seems the only natural beginning. But most 
pupils have seen a butterfly, while comparatively few 
have seen a butterfly^s eggs. In most cases, though the 
egg would form a part of the teacher's mental content, 
it would not form a part of the pupil's, and therefore 
would not prove a suitable commencing element. 

On the other hand, if the teacher possesses specimens 
of the eggs of butterflies, he might quite well start with 
the idea of egg in general, which, of course, forms a com- 
mon element in teacher- and pupil-content, and then 
present the specimen eggs as new matter to be correlated 
with the old. Out of the common elements it is always 
the teacher's business to select those which will lead to 
the desired result with the minimum expenditure of time 
and energy. In certain subjects the difficulty of choos- 
ing the proper elements is much greater than in others. 
In mathematics, for example, there is much less liberty 
of choice than in, say, history and geography. The 
connection among the different points in the subject 



184 EXPOSITION AND ILLUSTRATION IN TEACHING 

is SO close that it is impossible to present them in any 
but one order. Yet even in mathematics there is great 
diversity of opinion as to the order in which certain 
elements should be presented. At what stage, for 
example, should the idea of an equation be introduced 
in the teaching of algebra ? Should decimal or vulgar 
fractions come first in the teaching of arithmetic? 
Again, the whole of the propaganda for what is called 
the new geometry is an exemplification of the impor- 
tance placed on the beginnings as determining the 
after processes. 

As there are many beginnings throughout the course 
of a lesson, so there are many endings. Every 
beginning implies an ending of the same degree of im- 
portance as itself. Naturally the ending of a lesson or a 
section has to be as carefully considered as the begin- 
ning. In point of fact, they must be considered together. 
Indeed it may be said that the end determines the begin- 
ning. The principle of the Zielangabe demands that 
the pupil shall know the end, at least in the sense of the 
aim or purpose. But the teacher must know the end 
also in the sense of the termination. He must know 
what his process is going to accomplish, and he must 
also know how his process is to terminate. He must 
know the end from the beginning, and further, he must 
correlate the beginning to the end. It is true that 
much may happen of a very unexpected character 
between the beginning and the end. It is in this inter- 
mediate period between the beginning and the end 
that the teacher^s individuality has most scope; but in 
order that he may make the best use of his opportunities, 
it is essential that at the preparation stage he should 
determine his beginning and ending. 



BEGINNINGS IN EXPOSITION 185 

There is nothing to prevent the teacher making the 
beginning that he fixes upon as best. The plan that 
he resolves upon in his study he can at once proceed 
to carry out in the class room. With the ending it is 
different. Too frequently the actual ending has little 
resemblance to the ending that had been projected. 
Sometimes in the course of a lesson the teacher dis- 
covers that he has made a mistake in his private review 
before the lesson. Occasionally it is a mistake in the 
subject-matter that he did not notice in his preparation, 
and that is only brought out in the process of teaching. 
More usually the trouble arises from the discovery that 
his pupils know less or more of the subject than he had 
given them credit for. In such cases it is essential 
that the predetermined end should be modified. But 
in all other cases it is highly desirable that the selected 
end should be reached. The teacher must be very elastic 
in his arrangements for meeting unexpected develop- 
ments in the course of the lesson, but he should be 
tenacious in his efforts to reach the predetermined 
stopping-place. Unforeseen difficulties may arise to 
disturb the prearranged distribution of time, and the 
teacher may thus not get within reasonable distance of 
the point at which he had resolved to close. This con- 
tingency should be provided for by selecting beforehand 
a series of possible endings throughout the course of the 
lesson, — the attainment of each Zwischenziel should 
be a possible ending, — and by cultivating a very 
tender conscience with regard to using them. The 
teacher should feel that every time he has to adopt one 
of those alternative endings he has made a blunder 
in his calculations. On the other hand, to persist 
doggedly in getting to a prearranged end, whether 



186 EXPOSITION AND ILLUSTRATION IN TEACHING 

the pupils are able to follow or not, is worse than 
a blunder. 

In any case the point at which the lesson actually 
stops should be recognised by both teacher and pupil 
as a natural end. It must not be a mere cessation of a 
process, as in the case of a street organ that stops opera- 
tions in the middle of an air. Nor must the teacher 
merely allow himself to run down like a clock that grad- 
ually ticks more and more feebly till at last it stops. 
Nor must the end be reached by mechanical stages 
that the onlooker can anticipate. The mannerisms by 
which some teachers let it be understood that the end is 
approaching, frequently indicate rather the termina- 
tion of the hour than the end of the lesson. The true 
ending is felt to be an ending as soon as it is reached. 
At the end of a discourse it used to be the custom in 
France for the speaker to add the words, J^ai dit. At 
the end of an address arranged in the admirable form 
for which French speakers are noted, the words came 
as the inevitable conclusion. They were felt to be the 
only words that would not have been irrelevant at the 
point at which they were introduced. 

In every case the ending should find a natural place in 
the rhythm of interest. The predominant feeling at the 
ending points should be one of satisfied interest; but 
this satisfaction should be unstable. The interest in the 
particular section should be exhausted, but the interest 
in the wider whole of which the section is a part should 
be maintained. The interest to be carried forward 
should belong to the section that is to come, not to that 
with which the lesson finished. 



CHAPTER VIII 

Order of Presentation 

It is one thing to acquire knowledge for oneself; 
it is quite another to communicate that knowledge. 
When we say we have mastered a subject, we mean that 
we have not only amassed all the available matter, 
but have rearranged that matter so as to have it in an 
organised form, in which each element occupies its true 
relation to all the others. Teachers are apt to rest 
satisfied when they have reduced their mental content 
to this logical order, and to think that they have nothing 
further to do than to present the matter in the order to 
which they have reduced it. Many teachers will admit 
having had something like the following experience. 
When preparing for the first time a scheme for a sys- 
tematic course in a certain subject, the thought forces 
itself into the mind: ^'Why wasn't I taught this sub- 
ject in this logical way ? When I was a pupil, the matter 
always appeared to me as a thing of shreds and patches : 
I shall take care that my pupils are taught differently.'^ 
The cause of the trouble is that we are confusing know- 
ledge in its ripe and in its green state. The logical point 
of view necessarily implies a complete knowledge of the 
field to be covered. It represents the view that we 
may take of an experience that we have had, which is 
never quite the same thing as the anticipation of the 
experience we are going to have. The learner is feehng 

187 



188 EXPOSITION AND ILLUSTRATION IN TEACHING 

his way into a region that is already well known to the 
teacher, who must, therefore, modify his presentation to 
meet the needs of the pupil rather than to satisfy the 
demands of logical sequence. 

It is natural that we should suppose that logic ought 
to determine for us the order in which matter should be 
presented; but experience has shown teachers that they 
must not depend too much on logical arrangement in 
presenting matter to young people. Even when dealing 
with grown-up, educated people, it is necessary to be on 
our guard against a too rigid adherence to logical pres- 
entation. In describing to teachers how the struc- 
ture of animals should be taught, Sir Archibald Geikie 
interrupts himself to remark : — 

'Tor the sake of logical sequence, I have placed the consideration 
of form before that of function. But in actual practice it will 
not be always possible, even were it desirable, to separate these two 
subjects sharply from each other. " ^ 

It may be logical to complete an account of the struc- 
ture of an animal before saying a word about the 
functions of the various parts, but it is certainly not 
the best mode of exposition. The head of a London 
training college, in dealing with grammar, tells us : — 

" Obviously the psychological order (and that is the order to be 
followed in school-teaching) is (1) the acquirement of the use of 
language ; (2) the analytical investigation of language — that is, 
grammar. But, it might be argued, grammar deals with the 
presuppositions of language, and therefore the logical order is 
(1) grammar ; (2) the acquirement of language. Teachers have^ how- 
ever, discovered as the result of much unproductive labour that it is 
impossible to adopt the logical order in teaching children. When, 
indeed, the pupil has reached a certain stage in the acquirement of 

* The Teaching of Geography, p. 109. 



ORDER OF PRESENTATION 189 

the use of language, then grammar may be a means of helping him to 
increase his mastery; but it is impossible to begin that way.'' ^ 

Still, it must not be supposed that even in dealing 
with young people there is something objectionable in 
logical sequence in itself. On the contrary, the logical 
sequence represents the ideal order which must be 
followed as far as that is possible. Every deviation 
is a concession to human weakness. For the teacher, 
the logical sequence of the facts to be dealt with is the 
beginning of the process of Exposition : for the pupil, it 
is the end. 

In his essay on the Philosophy of Style, Herbert Spencer 
seeks for a general principle underlying all the recog- 
nised rules for verbal expression, and finds it in ^Hhe 
importance of economising the reader's or hearer's 
attention.'' ^ Every time we use the wrong word or the 
wrong order of words, we cause certain wrong combina- 
tions to be formed in the mind of the pupil, and the 
necessary correction of these errors is sheer waste of 
time and energy. Spencer does not go into the mot 
propre theory that for a given place in a given sentence 
there is one word, and one word only, that will perfectly 
meet the case; but he comes near to maintaining an 
equally rigid principle for the order of words in a sen- 
tence: '^We have a priori reasons for believing that in 
every sentence there is some one order of words more 
effective than any other." ^ 

Even when a sentence is grammatically correct and 
is ultimately intelligible, it may have its parts so badly 
arranged that an altogether disproportionate amount 

^ L. Brackenbury : The Teaching of Grammar, p. 7. 

2 Essays, Stereotyped Edition, Vol. II, p. 11. 

3 75^-^^^ p, 16, 



190 EXPOSITION AND ILLUSTRATION IN TEACHING 

of time and effort must be expended over it. Both of 
the following sentences by English authoresses of some 
distinction exemplify bad order of presentation : — 

" I am sure, too, the reputed Hibernian has afforded much inno- 
cent amusement who, on making his first journey, asks why, if it be 
true that the last carriage is, as he has been told, dangerous to travel 
in, it is not taken off.'' 

"The crowd of faces congregated round her, and from its midst 
emerged the one she shunned supremely ; his whose, while her will 
remained, she must with the last remnant of it, shut away." 

It is probable that Spencer carries his theory into too 
great detail. For example, he prefers the English order 
''black horse '^ to the French '' cheval noir.''^ In all 
probability in both cases the two words are simulta- 
neously received by the mind, and the figure of the 
animal occurs as accurately to the Frenchman as to the 
Englishman. For it has to be noted that Spencer in his 
essay takes it for granted that all thinking is figurative. 
His view is that if we mention the horse first we at once 
make a picture of it, and since we are not guided as 
to its colour we are more likely to make it brown than 
black, because there are more brown horses than black 
ones. When the word black occurs, we have to recolour 
our mental horse, and in this way lose time and waste 
energy. 

Spencer should have gone farther with his contrast 
between the black horse and the cheval noir, for the 
French have certain very definite customs in the matter 
of the order of their adjectives. The underlying prin- 
ciple appears to be that if the quality is inherent in 
the substantive, the adjective should precede; while 
if it is an accidental quality, as colour or nationality, 
it should follow. " Voire aimable fille " is a compliment 



ORDER OF PRESENTATION 191 

not only to your daughter but to you and her sisters. 
^'Votrefille aimahW^ is still a compliment to this par- 
ticular daughter, but at the expense of her sisters and 
of yourself — it is no longer taken for granted that ami- 
ability is innate in your family. The French have thus 
a means denied to us of conveying a distinction, and it 
is not likely to be maintained that French thinking 
is retarded in consequence. 

Whatever may be true about the possibility of simul- 
taneously grasping the meaning of a substantive and 
its adjectives, there can be no doubt that when we come 
to larger divisions of thought process, great differences 
occur according to the order in which elements are 
presented. The total effect of a presentation is not 
necessarily the same in two exactly similar cases be- 
cause precisely the same elements have been used in 
each. The order in which the elements have been 
presented counts for something, frequently for a great 
deal. An excellent example is to be found in the loss 
of cumulative effect when a series of elements is pre- 
sented without regard to their degree of stimulating 
power. A passage may exemplify the rhetorical figure 
of climax, or may convey merely an unpleasant effect of 
mental jolting, according as the elements are arranged 
in regular order of stimulus or '^just as they come.'' 

It may be suggested that the effect here is rather 
aesthetic than intellectual, and it may be asked: Is it 
not possible that the same intellectual effect may be 
secured by quite different orders of presentation? 
As a matter of fact, it may be urged, we have practically 
all of us gained our present knowledge and opinions 
by different lines of study and experience. No two 
of us have had our mental content presented to us in 



192 EXPOSITION AND ILLUSTRATION IN TEACHING 

quite the same order. This has to be admitted. But on 
the other hand, it will hardly be denied that, however 
our knowledge has been acquired, no two among us have 
quite the same mental content, and even if it were 
possible that two of us should turn out to have the same 
mental content so far as matter goes, the arrange- 
ment of that matter would be almost certainly different. 
Mathematicians are usually quite willing to spare a 
little time to show the excessively remote chances of 
mental coincidences of this kind. We are what we are, 
not merely because we know what we know, but because 
we possess our knowledge in a particular way. 

It is true that even if we have been badly taught we 
may have corrected the errors into which we have fallen, 
and have now reached the same stage as others who 
have been better taught, and have therefore reached 
their present stage with less difficulty. But it is at 
least arguable that in the process of being badly taught 
the pupil has received permanent injury, as well as 
suffered loss of time and energy. It may be that our 
present state of knowledge in any subject may bear 
definite traces of the process by which that knowledge 
has been acquired. In one of his Essays, Grant Allen 
tells us that at every moment we are shutting out one- 
half of the possibilities of life, that every choice we make 
is a dichotomy. The accompanying diagram may re- 
present Grant Allen's view. Starting from A we may 
reach K by Si series of four dichotomies. We may ob- 
viously pass from A to i^ in various ways. We may 
take the upper passage ABGHK, or the lower ACFEK; 
or we may take a zigzag course ABDHK or ABDEK. 
The important point for us to consider is whether the 
result when K is reached is the same in all cases, nor 



ORDER OF PRESENTATION 193 

matter what the route has been. The conclusion seems 
inevitable that the route does modify the result. Take 
the German possess! ves ihr = her, and sein = his. To a 




pupil who approaches this matter from the standpoint 
of English there need never be any confusion between 
ihr and sein; the gender of the substantive possessed 
only affects the words to the extent of modifying the 
termination. To an English-speaking pupil, however, 
who approaches the subject through French there is 
frequently a long period of struggle with the confusion 
that results from the fact that in French sa may mean 
Msj and son may mean her. Experience shows that in 
book-learned German this confusion persists long after 
a clear statement of the facts has been thoroughly 
understood by the pupil. He has an intellectual per- 
ception of the facts of the case quite as clear as that of 
his fellow who has made the English approach, but he 
does not know them in quite the same way. 



194 EXPOSITION AND ILLUSTRATION IN TEACHING 

The very adjective used above, ^'book-learned/' in 
itself either begs the question or proves that a fact 
learned from a book is not quite the same thing as the 
same fact learned in some other way. The balance 
certainly appears to incline towards the difference of the 
result according to the means of obtaining it. Pupils 
who have suffered from bad exposition, nearly always 
retain a certain lack of confidence in the use of matter 
that has been thus presented to them.^ They are apt 
to bring in as part of the completed whole certain com- 
binations that occurred where they had no right to 
occur in the original process of presentation. They 
were explained away, no doubt, at a later stage, but 
they have left their traces. 

Even in simple narrative the order of presentation is 
important to a proper understanding of the point to be 
brought out. Here the mere time order in which the 
events occurred is usually sufficient to determine the 
order of presentation. When the careless story-teller 
breaks in upon his narrative with the apologetic: ''Oh, 
by the by, I forgot to tell you — " it means that he has 
bungled his presentation. It does not as a rule mean 
that he has forgotten some unimportant detail, but that 
he has suddenly found that he has omitted an important 
section without which the whole is meaningless. He 
has accordingly to break the current of interest, and 
generally succeeds in confusing the impression on the 
listener's mind. This does not mean that the listener 
does not catch the point of the story, but that the point 

* The ihr and sein difficulty may entirely disappear under the in- 
fluence of constant use of German, but let a discussion arise about a 
particular case and the old doubt will sap the confidence of the victim 
of confused presentation. 



ORDER OF PRESENTATION 195 

has been blunted. In order to illustrate the fact 
that illiterate people may form a just estimate of the 
^'values" of a picture, a lecturer told the story of the 
English lady who was accompanied by her maid while 
visiting a certain Italian church in which there was 
a very fine picture of the Flight into Egypt. Talking 
down to the intelligence of her maid, the lady asked if 
she did not greatly admire the oleanders in the picture. 
The reply contained an unintentional reproof: ^'I 
wasn't thinkin' o' the oleanders, but o' the 'oly family." 
Unfortunately in using the illustration the lecturer began 
the maid's reply, '^I wasn't thinking o' the 'oly family, 
but — " Though he caught himself up at once and 
reversed the order, the point was ruined. No amount of 
emphatic explanation could produce the clear-cut effect 
the illustration had produced on previous occasions. 
The audience understood the point all right, but its 
effect was gone. 

The general line of presentation is practically deter- 
mined by the beginning, since this in its turn is deter- 
mined by the purpose of the exposition, as was shown 
in the last chapter. We are assumed, therefore, to 
know (1) the purpose we have in view, (2) the part of 
the pupil's mental content that is relevant, and (3) the 
new material we propose to use. The question now 
arises : In what order is the presentation to be made ? 
It may be objected that it is hopeless to discuss such 
a question apart from the nature of the particular 
matter, as this would seem to court error by omitting 
the most important element. But while the details of 
presentation must always be determined by the needs of 
each particular case, there is a certain body of general 
principles that are applicable to all cases, and give us 



196 EXPOSITION AND ILLUSTRATION IN TEACHING 

some guidance in dealing with each new set of circum- 
stances. It is true that these principles are of a some- 
what general nature, and indeed they are sometimes so 
vague as to amount to little more than pious aspirations, 
'' Instruct so that the matter given shall be learned" 
does not seem to carry us very far; nor does it greatly 
improve matters to add — '' and so that its culture 
content may exercise its due influence." ^ 

But certain principles that bear directly on the order 
of presentation have recommended themselves to 
teachers generally, and have obtained very wide rec- 
ognition, perhaps because of their very obviousness. 
The same interest in presentation that led Herbert 
Spencer to seek for the underlying principle of literary 
expression induced him to set forth in his little book on 
Education ^ those fundamental principles. It is not 
suggested that he originated them, and it is not our 
present business to trace each of them to its source. 
We are mainly interested in the possibility of their 
application in our work, and it is convenient to have 
them in the clear way in which they are presented by 
Spencer. 

There are six of these principles in all, but only the 
first three and the fifth concern us here. They run: 
In Education we should proceed (1) from the simple to 
the complex, (2) from the definite to the indefinite, 
(3) from the concrete to the abstract. (4) '^ The educa- 
tion of the child must accord, both in mode and arrange- 
ment, with the education of mankind considered histori- 
cally." This is clearly not germane to our present 
purpose; but from it is drawn a principle that is im- 

^ Otto Wilmann : Didaktik als Bildungslehre, Band II, p. 64. 
' Intellectual Education, Chap. II. 



ORDER OF PRESENTATION 197 

portant to us. As a special case of this fourth principle 
comes the fifth. (5) We must proceed from the empiri- 
cal to the rational. (6) '^Self-development should be 
encouraged to the uttermost " is now very generally 
accepted, but like principle number four it has no direct 
bearing upon our subject. 

In the very severe criticism to which Spencer's book 
on Education has been subjected, it is interesting to find 
that these general principles have met with the least 
opposition. They have not indeed escaped altogether, 
but most of the objections raised are concerned with 
the meaning attached to certain terms, and the critics, 
after they have made their protest, practically restate 
what Spencer wanted to say,^ though his mode of ex- 
pression did not quite meet with their approval. For 
example, we are left a little in doubt whether he meant 
his principles to be principles of education, or merely 
principles of teaching. As a matter of fact he lets us 
understand that he is dealing with the order of develop- 
ment of the mind, and since Exposition ought to follow 
that order, the two positions, the educational and the 
expository, ought in his opinion to coincide. 

It will be generally admitted that we ought to pro- 

^ The same is true about the general criticism of the principles 
themselves, apart altogether from their connection with Spencer, 
Their blatant obviousness seems to urge critics to find fault with them. 
This is what Tusikon Ziller has to say in his Allgemeine Pddagogik : 
p. 262, "... und so falsch der Grundsatz war, das im Unterrichte 
vom Einfachen zum Zusammengesetzen fortzuschreiten sei, ebenso 
falsch ist der andere vulgare Grundsatz, dass vom Bekannten zum 
Unbekannten fortgeschritten werden miisse." Then he proceeds, 
as one expects, to explain that he does not quite mean what he says. 
He does not seek to reverse the principle, but merely to bring out what 
it really means. We advance not from the known to the unknown, 
but to the presently unknown " mit Hiilfe des Alten und Bekannten." 



198 EXPOSITION AND ILLUSTRATION IN TEACHING 

ceed from the simple to the complex, though disputes 
naturally arise regarding what is simple and what com- 
plex. Spencer's meaning is made plain in his own words : 
^' Not only that we should proceed from the simple to the 
combined in the teaching of each branch of knowledge; 
but that we should do the like with knowledge as a 
whole/' ^ Thus stated, the principle would preclude 
the exposition of a complex by means of analysis; 
we would seem to be limited to synthesis in our teaching. 
But it may readily happen that the pupil knows a com- 
plex quite well, and yet is ignorant of the elements of 
which it is composed. A man may know what prose 
is and be able to use it effectively, without knowing the 
elements of which it is composed and the laws of their 
combination. No doubt in acquiring the mastery of 
the use of prose the man followed the general principle, 
but in Exposition it is surely legitimate to reverse the 
process. A pupil may know the rule for dividing 
vulgar fractions, and may be able to apply it with great 
effect. He follows his instructions to ^ invert the di- 
visor and proceed as in multipHcation," and gets the 
desired result. He knows the rule as a complex,^ but he 
may not be aware of the elements out of which the rule 
is built. 

In such a case the expositor may well proceed from 
the complex to the simple. There is sometimes a little 
confusion between the simple in itself, and the simple to 
understand. Spencer is aware of this danger, and warns 

^ Education, Chap. II, p. 65 (cheap edition). 

2 Of course it may be quite reasonably objected that a well -taught 
boy ought not to have this complex; but granted that the pupil has 
been badly taught, the expositor's best plan is to work from the re- 
sults already attained, however bad they may be. 



ORDER OF PRESENTATION 199 

teachers that ''a generalisation is simple only in com- 
parison with the whole mass of particular truths it com- 
prehends — that it is more complex than any one of these 
truths taken singly/' ^ and thus he feels the necessity 
of laying down the " concrete to abstract principle." 
With this rule the teacher need have no quarrel, since 
it will he found to be impossible to break it. It is true 
that attempts have been made to teach in the reverse 
order, and to pass from the abstract to the concrete. 
Indeed, for centuries teachers believed that they were 
teaching from the abstract to the concrete. They 
taught Latin by laying down rules and then setting their 
pupils to apply these rules. The pupils learnt Latin, 
no doubt, but not because of the rules they learnt. They 
did not understand Latin because of the rules, but the 
rules because of the Latin. The teachers did not really 
teach at all. What they did was to provide means by 
which Latin might be learned, and then to place their 
pupils in circumstances in which it was unpleasant not 
to know Latin. The master thought he was teaching 
from the abstract to the concrete, but the pupils actu- 
ally learned from the concrete to the abstract. It is 
impossible to learn in any other way. The abstract is 
necessarily unintelligible unless it has been reached by 
means of the concrete from which it has been derived. 
With an entirely new abstraction in relation to an 
entirely new bit of the concrete the mind can work in 
only one way. The concrete must precede. But in 
ordinary experience cases of pure abstraction are rare. 
We nearly always know something about the materials 
from which abstraction has been made, and the mind 
passes from what it knows of the concrete to deal with 

^ Education, Chap. II, p. 67. 



200 EXPOSITION AND ILLUSTRATION IN TEACHING 

the abstraction that is presented to it. From the ab- 
stract statement ^'Things that are equal to the same 
thing are equal to one another" the pupil may be made 
to pass to the concrete case that if Tom is the same 
height as James, and William is the same height as 
James, then Tom is the same height as WilUam. But 
the abstract statement, so far from making clear the 
equahty in the height of Tom and William, would not 
be even intelligible to the pupil but for many similar 
measurements that have been made in his experience 
before the abstract statement was heard of. Indeed, 
is it not a contradiction in terms to maintain that one 
can understand an abstraction without first knowing 
the something from which the abstraction has been 
made ? 

The truth is that in ordinary life there is a constant 
alternation between the abstract and the concrete in the 
process of acquiring knowledge. By careful examina- 
tion of the concrete we reach a certain abstraction; 
but we at once proceed to apply this abstraction by 
making a new connection with the concrete. As the 
result of abstraction from many concrete cases Mill 
enunciates his canons. Forthwith he exemplifies them 
by means first of letters, and then by still more material 
examples. He appears to be teaching from the ab- 
stract to the concrete, but in so far as his abstractions are 
understood at the first presentation, they are under- 
stood in terms of the concrete experience of the pupil. 
Logical presentation is possible with pupils who have a 
wide though ill-arranged knowledge of the subject. 
Grammar, for example, may be taught in logical order to 
a person who has a really good working acquaintance 
with the language in connection with which it is to be 



ORDER OF PRESENTATION 201 

taught. The very limitation here involved is sugges- 
tive. The language assumed to be known forms the 
necessary concrete. 

In many cases the facts to be presented are of coordi- 
nate rank and may be brought forward in almost any 
order. Take the different kinds of subordinate clauses 
as these are dealt with in the analysis of sentences. 
It does not matter much whether we begin with the 
Noun Clause, the Adjective Clause, or the Adverb 
Clause, on the understanding that the pupils have 
already mastered the Parts of Speech and are familiar 
with their functions. On the other hand, if gram- 
matical construction is being approached by means of 
the Analysis of Sentences instead of by Parsing, then 
it might be desirable to begin with the Noun Clause 
rather than with either of the others. Indeed, when the 
teacher comes to the point of choosing the order of 
presentation, he will almost always find that there is 
some one order that for some reason or other ought to 
be preferred. Further, this order is not a permanent 
one. Next time he has to deal with the same matter, 
but with a different class, he may find that a different 
order is preferable. The different clauses of Magna 
Charta are to a certain extent coordinate. They form 
part of the one great document. But their order of 
presentation would be different under different circum- 
stances. For example, if we are considering the docu- 
ment merely as a document, — as a specimen in the 
science known as Diplomatic, — the clauses would be 
dealt with in the order in which they occur on the 
parchment. In general constitutional history the clauses 
would be presented in their order of importance to the 
constitutional history of the country. We might either 



202 EXPOSITION AND ILLUSTRATION IN TEACHING 

begin with the least important and work up to the 
most important, or we might reverse that order. On 
the other hand, if our main purpose is to illustrate some 
special point — say the position of the artisan class 
in the Thirteenth Century — our presentation might 
centre round one point, say the term Contenement} 
If our interests are mainly in commercial matters, the 
clauses dealing with weights and measures and personal 
freedom of movement from place to place might come 
in the first rank. 

It not infrequently happens that in expounding a 
particular subject there are two or three terms to be 
explained, and the whole subject cannot be properly 
understood until these subordinate terms are made 
clear. Sometimes lengthy expositions of these sub- 
ordinate terms are given, while the whole process of 
understanding the main subject is suspended. Occa- 
sionally this is inevitable. But we must regard it as a 
danger signal when we have to introduce some such 
statement as: '' Before we can proceed to the considera- 
tion of the subject at issue it is necessary, et cetera, 
et cetera.'' Every time we interpolate explanatory 
matter we must satisfy ourselves that there is no more 
suitable place for it ; and when we see no way of avoiding 
the interpolation, we must do all we can to prevent its 
materially interfering with the flow of the main line of 
thought. 

^ " A freeman shall not be amerced for a small fault, but after the 
manner of his fault; and for a great crime according to the heinous- 
ness of it, saving to him his contenement ; and after the same manner 
a merchant, saving to him his merchandise." Then the explanation 
is in place : Contenement signifies the chattels necessary to each man's 
station, as the arms of a gentleman, the merchandise of a trader, the 
ploughs and waggons of a peasant. 



ORDER OF PRESENTATION 203 

We must always try to keep our subordinate ex- 
planations closely connected with our main subject, 
and with each other. In order to explain A, of which 
the pupils know a little, we may have to explain X and 
Y, of which they know less. We must guard ourselves 
against leaving A and Y quite isolated while we plunge 
into long explanations of X. We must adopt at least a 
working explanation of Y while we are elaborating X, 
else the bearing of X upon A will probably be obscured. 
This will be better understood by an example; the 
writer quoted is expounding the nature of Narrative: — 

^^A narrative is a representation of a series of events. This is 
a very simple definition; and only two words of it can possibly 
demand elucidation. These words are series and event. The word 
event will be explained fully in a later section of this chapter : mean- 
while it may be understood loosely as synonymous with happening. 
Let us first examine the exact meaning of the word series. 

The word series implies much more than the word succession: 
it implies a relation not merely chronological but also logical ; and 
the logical relation it implies is that of cause and effect. . . ." ^ 

Then the writer goes on for seven pages elaborating the 
meaning of this term series, before he begins to treat of 
the parallel term. But thanks to his thoughtfulness in 
supplying us with a working definition of event, we are 
able all the time we are considering series to make use of 
both this term and the term event to help us in under- 
standing what the expositor is telling us about nar- 
rative. 

This anticipatory treatment in which we refer to cer- 
tain aspects of a subject before we actually deal with 
them in detail is applicable on a large scale. In plan- 
ning out a book, for example, the same principles obtain 

^ Clayton Hamilton : Materials and Methods of Fiction, p. 44. 



204 EXPOSITION AND ILLUSTRATION IN TEACHING 

as in planning out a chapter. We are working with a 
different size of unit, but the principle is the same. This 
may be illustrated by reference to the idea of unit 
itself as treated in this book. In Chapter II we have 
a general reference to the idea of the unit of Exposition, 
in which it is treated in connection with the need for 
destructive process in preparation for constructive. 
Then again in Chapter IV we have the unit regarded as 
a part of a background, where we have to deal with it 
at the stage of complexity at which we find it. Finally 
in Chapter XII we have a new view of the unit. In that 
chapter it is used for purposes of comparison. Instead 
of being something to be analysed out, or to be used as a 
brick to build up with, it is to be used as a standard 
by which quantities of all kinds may be measured. It 
may naturally be objected that it is bad presentation 
to separate thus the different aspects of the same sub- 
ject. Why, it may be asked, does not the writer say 
all he has to say about the unit in one place, and have 
done with it? But it is all a matter of emphasis. 
If in planning the book the writer had determined to 
lay great stress on the notion of the unit as such, then 
he would have devoted a chapter to this subject, and 
in that case the contents of some of the other chapters 
would have had to be distributed throughout the book, 
as the unit has been under the present arrangement. 
But even when a special chapter has been set apart for a 
certain subject, it sometimes happens that an aspect of 
that subject is better treated in some other connection. 
Thus though there is a chapter (XIV) on the Picture, 
this is limited to the use of the picture as illustration. 
In Chapter IV some pages are devoted to the treatment 
of the picture, but here it is the mental picture that is 



ORDER OF PRESENTATION 205 

under discussion, the picture the pupil forms for him- 
self as the result of verbal description. In Chapter 
XIV we are dealing with the picture as something ob- 
jective, in Chapter IV as something subjective. 

The index of any book one takes up supplies many 
illustrations of the distribution throughout the text of 
the treatment of certain subjects that the reader might 
prefer to have had grouped together in one place. But 
apart from the fact that we cannot have a book ar- 
ranged according to the desires of each reader, it has 
to be remembered that there is a certain compensating 
advantage in treating the same matter at different 
stages, and in different connections. There is an ad- 
vantage in familiarising the mind of the reader with a 
given fact before that fact is brought forward for more 
or less exhaustive treatment. Novelists frequently 
introduce a fact two or three times in a very incidental 
way at the early part of the story in order that it may 
be the more effectively treated when its turn comes. 
This principle of casual introduction of matter to be 
afterwards elaborated may be used by the teacher in 
two ways. He may imitate the novelist and use this 
order of presentation in order to build up interest. 
Several illustrations will be found further on in this 
chapter, and in the next there occurs a deferred illustra- 
tion of a generalisation from Herbert Spencer quoted 
in Chapter III. It will probably be felt that this illus- 
tration is not only useful where it is, but that it has an 
increased force in relation to its original generalisation 
because of the delay. 

[This paragraph, within brackets, is deliberately in- 
troduced in order to explain its own vices in relation to 
the principles of Presentation. It is thrust in, you will 



206 EXPOSITION AND ILLUSTRATION IN TEACHING 

observe, between two sections. The teacher uses a 
novelist's device in two ways: one of them has been 
dealt with, the other is yet to come, and this paragraph 
is thrust in between them. This is bad, and is only 
justifiable because it emphasises a defect by calling 
attention to it at the very moment when it is producing 
its irritating results. The paragraph originates really 
in the desire to call immediate attention to a blunder 
in presentation that has just been made. While it is 
excellent to refer to something that has already occurred 
in a book, it is generally a mistake to refer specifically 
to what has not yet been reached. In the preceding 
paragraph the reader is practically invited to turn to 
the next chapter and read a particular passage, which 
he is then to compare with a passage in Chapter III. 
This not only seriously interferes with the reader's line 
of thought in this chapter, but spoils the effect of the 
passage he is invited to read. That passage occurs 
in a certain connection, where it is assumed it ought to 
occur. To read it in the first instance apart from this 
connection is obviously to do it injustice. It is quite 
different in cases where we are referring back to passages 
that have been read in their proper order and are now 
considered in a new connection. The same objection 
does not lie against the reference in the previous para- 
graph to Chapter XIV. There is in that case no call to 
turn to Chapter XIV at all. Its very title conveys all 
the information necessary to understand the reference 
in the text. After reading in typoscript the above de- 
plorable divagation, my colleague. Dr. T. Percy Nunn,* 

^ This does seem a most inopportune place, but in the absence 
of a preface I have no other; — I want to express mj'^ indebtedness to 
Dr. Nunn for his kindness in reading through, in the very limited time 



ORDER OF PRESENTATION 207 

SO far from helping me to return to the straight path, 
led me into temptation by sending me his copy of a 
work by that Master of Exposition, Sir Oliver Lodge. 
I looked into the book ^ and was lost. Sir Oliver's words 
in the Preface form an admirable commentary on what 
I have already written : — 

''Since the book is intended to be useful to the higher class of 
students, it seemed very permissable to adopt a method which I al- 
ways use in teaching ; viz. to begin by giving some ideas at first, 
and to gradually polish them up later, rather than by attempting a 
too highly finished statement ab initio to overburden and depress, 
and possibly to confuse, a student. Because of this progressive 
arrangement, I may be permitted to urge students to read the book 
through before proceeding to dip into it by help of the index, and 
before taking notice of references forward which subsequently it is 
hoped will prove useful.""^ (Italics mine, to emphasise the applica- 
tion to the present book.) 

Naturally the same principles may be applied in oral 
Exposition, but with a greater sense of responsibility, as 
the pupil is entirely in the expositor's hands.] ^ 

The second use the teacher may make of the inciden- 

just before going to press, the typescript of this book, and for the 
really valuable criticism and help he gave. 

^ Modern Views of Electricity. 

2 Those who are interested in the presentation of this subject will 
find in Modern Views of Electricity examples of "anticipations " and 
"references forward" on pages 16, 17, 28, 42, 90, 94, 96, 98, 99, 105, 
128, 144, etc., of the first edition, 1889. For an interesting illustration 
of the preparation for a subject by incidental reference to it in order 
gradually to build up an interest in it, see Sir Oliver's treatment of 
the topic "Does electricity possess inertia?" in sections (not pages) 
7, 42-48, 88, 89, 98, 105. 

2 On re-reading the above paragraph illustrating defective arrange- 
ment it strikes me that I have rather overdone it. We could hardly 
have a worse case of congestion : but I let it stand, as the reader's 
irritation will only emphasise the lesson meant to be conveyed. 



208 EXPOSITION AND ILLUSTRATION IN TEACHING 

tal introduction of some matter before it is really wanted 
is exactly the opposite of the novelist's. He may seek 
to exhaust the intrinsic interest of matter that is to be 
afterwards used as illustration. By introducing the 
attractive matter in unimportant places, he allows the 
pupil to enjoy its interest for its own sake, and when 
this has been repeated two or three times, the pupil 
is ready to take a new point of view from the teacher, 
and get up a secondary interest at the proper place.^ 

Sometimes the order of presentation is determined by 
very practical considerations. In preparing hydrogen it 
makes some difference whether the pupil is told to pour 
in the water before he is told to pour in the sulphuric 
acid. In that form of practical presentation commonly 
known as ^'directions," when supplied along with 
machines, implements, or commodities, the order of 
presentation is of vital importance. I have seen the 
pointer of a typewriting machine broken because the 
direction, ''Be careful to lower the pointer when re- 
placing the carriage" occurred after the instructions, 
" How to replace the carriage." At the head of every 
set of practical directions should appear the caution: 
Please read the directions right through before beginning to 
, etc. 

This naturally raises the question of the help that 
one part of a presentation gives to another. It may 
happen that what is obscure when only two elements 
have been presented becomes quite clear so soon as a 
third element is brought forward. This involves the 
problem of suspended understanding during a process 
of presentation. Is it justifiable to present at a given 
time certain matters that cannot possibly be under- 

^ This is further dealt with in Chap. XVI, p. 391, 



ORDER OF PRESENTATION 209 

stood by the pupils till at a later stage additional matter 
is supplied ? If it is a case of presenting matter that 
cannot be understood at all at a particular stage, but 
must be got up by memory for use later on, it will 
probably be agreed that the presentation should not be 
made. It is different, however, when the presented 
matter cannot be fully understood at the time of pre- 
sentation, but will be fully understood when additional 
matter is presented at a later stage. Almost all our 
presentations are open to the objection that the matter 
brought forward cannot at the moment be fully under- 
stood. All that we can hope for is that it may not be 
misunderstood. From the material supplied, the pupils 
may make premature conceptions that must after- 
wards be painfully destroyed in order to make way for 
the correct construction. It is not uncommon to hear 
post-graduate students who are being trained to teach 
the elementary subjects confess that they never under- 
stood the true meaning of what is called simple sub- 
traction till they saw the subject taught in the demon- 
stration school. They often find that they have to 
break down and reconstruct all their idea combinations 
on the subject. So with pupils who have been taught 
scansion or music on purely mathematical lines: there 
comes a period of necessary reconstruction when they 
reach the stage of artistic appreciation. Pupils who 
have had drawing presented to them as a system of fine- 
line copying from the flat have to fight very hard indeed 
before they can break up the false combinations and by 
reconstruction attain the freedom to use drawing as a 
means of expression. Doubtless the reader's own edu- 
cation furnishes him with more than one illustration 
of this need for reconstruction. There are cases, as we 



210 EXPOSITION AND ILLUSTRATION IN TEACHING 

shall see later in the chapter, in which this formation 
of premature conceptions and their correction may be 
turned to good account, as a means of strengthening a 
desired aesthetic or moral effect. But on the cognitive 
side we must do all we can to secure the correct (not 
necessarily the complete) conception at the very start. 

Taking it for granted that certain orders of presenta- 
tion are more economical of the pupil's time and energy 
than are others, it may be objected that the teacher's 
business is not to save the pupil's time and energy, but 
rather to make him expend both. There are those who 
maintain that the best progress is made by the process 
of trial and error. The argument is that you know a 
thing better if you have made your blunders, and found 
out the truth for yourself. The result is more your own 
than if it had been pumped into you by a watchful 
teacher who stood by all the time to prevent the possi- 
bility of your going wrong. 

In all arguments of this kind there is a slight confu- 
sion of thought between the different parts of a teacher's 
work. The formation of character is one thing, the ex- 
position of a subject another. A man may often be a 
better, because a stronger, man on account of the diffi- 
culties he experienced in acquiring the knowledge he 
needed. But it does not follow that he knows his 
subject better because he had to study it under bad 
conditions. The argument of those who underesti- 
mate the value of careful teaching is that the pupils 
become emasculated, and unfit for any serious study. 
But surely it is idle to complain that we are doing too 
much for our pupils. There is a Hmit beyond which 
it is impossible to help them at all. Beyond that 
limit our help becomes a hindrance. To pass that 



ORDER OF PRESENTATION 211 

limit is clearly bad Exposition, but up to that limit 
the more we can help the pupil the better. There 
always will remain the irreducible surd of individual 
effort that cannot be eliminated by any amount of 
external help. 

On the other hand, there is the danger that some 
teachers may regard the giving of trouble as in itself a 
laudable thing. The implied argument is surely easily 
disposed of by a reductio ad ahsurdum. If the increasing 
of the difficulties of our pupils is an advantage, it 
would naturally follow that the worse our exposition 
the better for our pupils. The teacher who provided 
the worst text-books and made his pupils work under 
the worst conditions would do them most good. Some 
teachers actually adopt this attitude, and oppose the in- 
troduction of the metric system on the ground that 
their pupils would lose the enormous advantage of 
having to cope with those curious vestigial items 5| and 
30j that adorn our present arithmetical tables. In 
the course of a recent examination in Education as one 
of the subjects for a university degree, I set the follow- 
ing question : — 

" Speaking of the limited educational curriculum in the best days 
of Greece, Professor Bosanquet asks : ' How was so much made out 
of so little ? ' What answer would you suggest ? " 

A large percentage of the candidates took occasion to 
point out that the curriculum was not nearly so inade- 
quate as it appeared. The subjects studied had the 
advantage of several difficulties that are no longer 
available in our modern schools. For example, the 
Greek characters were not only made by the hand and 
therefore rather clumsy, but they were arranged with 



212 EXPOSITION AND ILLUSTRATION IN TEACHING 

no spaces between the words, and to separate out the 
individual words involved a great exercise of attention 
and ingenuity; while the fact that the Greek numerals 
were so awkward to deal with provided still further 
opportunities for strenuous training. 

The truth is that all this pother about the dangers of 
a soft pedagogy is based upon the assumption that it is 
possible to make teaching so perfect that nothing is 
left for the pupils to do. But all that the most skilful 
presentation can do is to prevent the pupils from 
having to waste their time in unprofitable ways of 
expending their energy; as, for example, in manipulating 
antique tables and separating words that should never 
have been united. The better the exposition the more 
rapid the progress of the pupils; the only limit to their 
progress under these conditions being, in fact, the neces- 
sary limits imposed by the need of time for consoli- 
dation. 

For it has to be remembered that a pupil cannot go on 
indefinitely piling up knowledge, no matter how skil- 
fully it may be presented. However brilliant the natu- 
ral parts of the pupil, and however skilful the expositor 
may be, there is a limit to the speed at which a pupil 
can master a subject. Even the plain practical man 
admits this, though with obvious regret. It is with 
reluctance that he acknowledges that we cannot put 
old heads on young shoulders. There are no doubt 
sound psycho-physical reasons why even an Isaac 
Newton requires a certain minimum of years before he 
can deal with certain mathematical problems. For our 
present purpose it is more important to observe that 
all mental processes involve a certain expenditure of 
time. Natural processes may be greatly accelerated in 



ORDER OF PRESENTATION 213 

a forcing house, but even in a forcing house a minimum 
time Hmit is imposed. Stupid pupils demand a long 
time/ but even the cleverest, when treated under the 
most favourable conditions, must have a minimum time 
to consolidate their gains. There is no fear of excessive 
speed through excellent exposition. 

The figure of the forcing house brings forward an- 
other aspect of the objection that deserves treatment, 
since there is a basis of truth underlying it. Some 
writers want to know whether, by this very carefully 
prepared exposition, we may not weaken the power 
of initiative of our pupils and make them incapable 
of learning anything for themselves. It is pointed out 
that certain schools that have specially laid themselves 
out to prepare pupils for examinations, have reduced 
the art of Exposition to such a state of formal perfection 
that nothing is left for the pupils to do. But cramming 
and Exposition are different things. The crammer's 
aim is to get his pupil to reproduce under unhealthy 
conditions a certain amount of information. He is 
not concerned how the matter is retained, so long as it 
is there when called for; nor whether it is understood 
or not, so long as it can be put down on paper without 
betraying any lack of comprehension. The aim of the 
expositor, on the other hand, is frustrated if the pupil 
does not understand the matter presented. But surely 
the more easily the pupil can be made to understand the 

^ Experienced coaches have great faith in the efficacy of time in 
removing difficulties. Dr. David Rennet, the distinguished mathe- 
matical coach at the University of Aberdeen, whose success in pre- 
paring for examinations is phenomenal, is sometimes encouraging to 
dull but earnest pupils when they are worsted by a problem even 
after it has been explained. His remark is :" Aweel, than. Ye must 
juist wait till it sipes [soaks] in." 



214 EXPOSITION AND ILLUSTRATION IN TEACHING 

better. It does not follow that the most direct recti- 
lineal exposition is the easiest in the long run. Every- 
thing has to be judged by the kind of understanding 
attained. But assuming that our aim is the highest 
form of understanding, then it may be taken for 
granted that the easiest way to attain that form is the 
best. To deny this is to assert that labour and trouble 
are in themselves desirable. If there is any suggestion 
about " their value as training, '' etc., it is a sufficient 
reply that all this is already discounted when we have 
accepted as our aim the highest form of result. It is for 
this reason that the expositor is entitled to use con- 
trast, and even contradiction, if he can show that these 
are better means of expounding his subject than 
straightforward presentation of facts that are easily 
assimilated. Under certain conditions it may be desir- 
able to go against the principle of economy on which 
Spencer lays so much stress. But in all such cases it 
will be found that we are keeping to the spirit of Spen- 
cer's principle, though we reject the letter. It is well to 
follow the line of least resistance, but naturally every- 
thing depends upon where one wishes to go. The 
means are relative to the end : it is another case of the 
longest way round being sometimes the shortest way 
home. 

When Nathan led the unsuspecting David to con- 
demn himself in the person of the robber of the one 
ewe lamb, he was supplying us with an excellent ex- 
ample of a ^'premature conception '' that had to be 
destroyed and reconstructed before the prophet's ex- 
position was successful. But obviously the result was 
worth the expenditure of time and energy. Indeed, it 
may fairly be said that to attain the result the prophet 



ORDER OF PRESENTATION 215 

had in view the roundabout way was the line of 
least resistance. An intellectual understanding of the 
case could no doubt have been secured in David's 
mind without this troublesome reconstruction, but the 
prophet wanted something more than mere intellectual 
consent. 

In Nathan's case the matter was so skilfully pre- 
sented that there was no room for error. The recon- 
struction was not called for till the very moment it was 
needed, and the first construction did not in itself in 
any way conflict with the effect of the second. But the 
greatest care is necessary to prevent the first construc- 
tion from making the second impossible. An amiable 
old gentleman was called upon to propose a vote of 
thanks to the chairman and governors of a great 
school at the distribution of prizes. Tired of the con- 
ventional way of doing what was expected of him, he 
thought he would introduce an agreeable variety by 
emphasising the brighter side of a governor's office. 
Accordingly he pointed out that though the duties of a 
governor were very exacting, and involved a great 
expenditure of time and energy, the governors were 
very well paid for it. He had intended to round off his 
speech with a glowing account of the joys of being kept 
young by constant contact with the fresh young life 
that he saw before him, and of being cheered by the 
glow of good work well done, and a number of other 
compensating satisfactions that come by way of re- 
ward to the conscientious governor. But at the mere 
words ^^well paid for it" there arose such a murmur 
of protest among the assembled governors that the re- 
mainder of the amiable gentleman's speech consisted of 
a hurried explanation that '^that is not what I meant." 



216 EXPOSITION AND ILLUSTRATION IN TEACHING 

This unhappy gentleman applied unskilfully an arti- 
fice that is quite legitimate in Exposition. He sought 
to create a vacuum for a fact that he proposed to pre- 
sent. He knew that his remark would excite a certain 
amount of surprise which would in its turn lead to a 
curiosity that he would then proceed to satisfy. He 
had not calculated on surprise passing over into indigna- 
tion instead of into curiosity. With the less personal 
issues raised in instructing in school it is often desir- 
able to apply this principle of the vacuum. If the 
teacher can create the desire for a particular bit of 
knowledge, he is on the way to the best possible pres- 
entation of that knowledge. The following example 
from actual teaching illustrates what is meant. It is 
taken from the essay of one of my students at the 
University of London: — 

" I was teaching a class to scan the hexameter line in Latin, and 
after teaching the division of the line into six feet, two beats in 
each foot made by either dactyl or spondee, and the invariable na- 
ture of the fifth and sixth feet, I put up some fines on the board for 
us to work out together. The pupils got on swimmingly for the 
first fine, as the lengths of the syUables were well known to them. 
But the second fine was : — 

* Mutat terra vices, et decrescentia ripas.' 

Working backwards, they arrived at all the feet except the first, 
and there they stopped in difficulty. Only two syllables were left 
for this foot, and they had been carefully taught that the third 
person singular present indicative of the four conjugations was short. 

Was the foot a trochee \j ? That was the time for the explanation 

of 'vowels long by position,' which would have been imperfectly 
comprehended if given before the children had found the difficulty 
for themselves." 

Leaving to specialists the decision of the question 
whether scansion should ever be taught in this way, 



ORDER OF PRESENTATION 217 

whether in direct or in inverted order, it is necessary to 
point out, what the student herself discovered after 
sending in the essay, that the appHcation of the vacuum 
here involved the fallacy of assuming that the pupils 
would make et long by position in order to get into 
difficulties at the end so as to be led to enquire into 
the very rule that they had already applied. The 
student's reply was that her plan worked: she desired 
to get the pupils into this difficulty, and she succeeded. 
Obviously the excellence of the plan is not diminished 
by the fact that a more suitable verse ^ was not chosen. 
The principle of the vacuum may be usefully applied 
in the introduction of new technical terms. If at the 
beginning of teaching geometry we speak a great deal 
about ^Hhe line joining the opposite angles of a square,'' 
the pupils will get tired of the cumbrous phrase, and 
when the term diagonal is introduced, will welcome it 
as a relief from the wearisome description. In science 
teaching, the principle may be applied by giving half a 
dozen applications of a certain rule, e.g, different phe- 
nomena resulting from the pressure of the atmosphere, 
without enunciating the rule till the last application is 
made. By this time the pupils want to know what is 
the cause of the peculiar phenomena they have seen, 
and are glad to have such an economical arrangement as 
one principle (whether given by the teacher, or, better, 
discovered by themselves) to explain half a dozen re- 

^ The verse — 

" Scindit se nubes, et in sethera purgat apertum " 

would have led to the desired result, and would have had the addi- 
tional advantage of including a third person singular (purgat) that 
follows the usual rule, and therefore emphasises the difference in 
scindit. 



218 EXPOSITION AND ILLUSTRATION IN TEACHING 

markable things that at first appear altogether different 
from each other. 

Sometimes the principle is more deliberately applied. 
A certain problem is stated, and various more or less 
plausible solutions are offered one after the other, 
and each dismissed in turn as unsatisfactory. But all 
through the discussion there is constant reference to the 
true theory. Phrases like the following are scattered 
throughout: '^as we shall see presently"; ''when we 
come to what we hold to be the true theory'^; ''as will 
be evident in the light of the theory about to be pre- 
sented; '^ "a natural mistake in a writer who has not 
the information that is about to be laid before you.'' 
For example, the lesson may be on those curious medal- 
lions that the antiquarians of the seventeenth and 
eighteenth centuries called contorniates. The un- 
skilled would naturally regard them as coins. People 
who know more are aware that this is not so, and various 
theories as to their nature have been held, such as 

(1) amulets to bring success to competitors at the games; 

(2) tickets to reserved seats at the games; (3) lots to 
determine the starting order in the chariot races; 
(4) medals indicating success in the games. Now the 
teacher starting with the view that the true use of 
contorniates was to serve as "men" in certain table 
games resembling our "draughts," keeps this in view 
all the time he is discussing the other theories, and takes 
every opportunity of shadowing it forth without actu- 
ally stating it. While pointing out all the difficulties of 
the other theories, he refers to " the better-supported " 
theory, "the clue is to be found in M. Froehener's 
brilliant suggestion," ^ "before what we believe to be 

^ Annuaire de Numismatique, 1894, p. 88 : quoted by K, A. Mac- 
dowall, in the Numismatic Chronicle, Fourth Series, Vol. VI. 



ORDER OF PRESENTATION 219 

the true solution was offered/^ By the time the Froe- 
hener theory is actually presented, a real need for it has 
been created. The pupil is tired of indirect suggestions, 
and welcomes the positive statement of the final theory. 

There is one limitation to the application of the prin- 
ciple of the vacuum in Exposition. The pupil should 
not be taught anything that is actually false. In using 
contrast and in preparing a vacuum, error is introduced, 
no doubt, but in the first place it is not taught as truth, 
and in the second place, the error is only relative. It 
must be associated with a certain amount of truth 
before it can have any value in a process that seeks to 
pass from apparent truth to a nearer approach to ulti- 
mate truth. There has to be reconstruction, perhaps, 
but the original construction is usually correct for some 
other set of circumstances, though unsuitable for the 
present. There can be no justification in presenting 
matter that is, so far as we know, false under all cir- 
cumstances. We want the pupil to get at the truth 
as it is known to us, and though we may find it desir- 
able to contrast his view of truth with ours, we need 
never present actual falsehood to him. 

We must distinguish between falsity and mere in- 
completeness in presentation. ''An instrument for 
telling the time^' is an incomplete, but not a false, 
definition of a watch. Many teachers are willing to al- 
low an incomplete presentation of ordinary terms, but 
draw the line when technical words are in question. 
Dr. T. Percy Nunn is frequently challenged by his 
students of the London Day Training College for giving 
''wrong" meanings to scientific terms. For example, 
he deliberately calls a mass of peroxide of lead, whatever 
its size, a "molecule," and when, under heat, it gives up 



220 EXPOSITION AND ILLUSTRATION IN TEACHING 

just the amount of oxygen to enable it to become lith- 
arge, he says it has given off one atom of oxygen, and is 
now a molecule of litharge, made up of one atom of 
oxygen and one atom of lead. This scandalises his 
young men, who have been brought up in the belief 
that size (or rather lack of size) is of the essence of mole- 
cules, and particularly of atoms. My colleague defends 
himself by maintaining that his meanings are not 
wrong, but merely incomplete. He believes that the 
qualitative approach gives the students a much better 
chance of getting the true meaning than does the quanti- 
tative. In the ordinary presentation the pupil is thrust 
into the middle of a theory before he realises the facts of 
the case. In very many instances he is so busy whip- 
ping up his imagination in the pursuit of the incon- 
ceivably small that he has no energy or interest left to 
attend to what, after all, are the essentials of the laws of 
chemical combination. It is always wise to begin with 
the proper point of view where it is possible, and in 
this case it is not only possible but actually easier than 
what may not unfairly be called the metaphysical 
approach. 

We should teach by good example rather than by bad, 
by showing what should be rather than by showing what 
should not be. Positive teaching is always better than 
negative. The ^^ awful example," as it is called, is bad 
exposition unless under conditions in which there is 
no doubt as to the right and the wrong. To write 
the word feild on the blackboard and enlarge on the 
heinousness of spelling it in that way only strengthens 
the chances of that form of the word reappearing in the 
pupils' exercise books. There is no self-interpreting 
standard compared with which feild will stand out as 



ORDER OF PRESENTATION 221 

inherently bad. In certain forms of symmetrical free- 
hand drawing, on the other hand, common errors made 
by the pupils may be with safety placed upon the black- 
board, since their very juxtaposition to the model will at 
once condemn them. There is here an objective stand- 
ard to which appeal may be made with no fear of 
misunderstanding. So with the objectionable para- 
graph on pages 205-207 of this chapter. It carries its 
own condemnation with it. 

In dealing with grammatical errors the type should 
be: '^The correct form is 'Charles and his cavaliers 
were defeated.' '' The emphasis on the were calls atten- 
tion to the fact that this is correct, without recalling 
the incorrect was of the exercise book. Even in a 
case of greater difficulty, where there might be room for 
a little argument, it is well to stick to the positive form. 
' ' Charles with his cavaliers was defeated. ' ' If the pupils 
themselves raise objections, a little argument may be 
permitted, but even then the repetition should always 
be of the correct form, and not of the alternative 
were, as suggested by the pupils. Reiteration of the 
right should be the expositor's principle rather than 
condemnation of the wrong. 

Some teachers set what they call mistake-traps, in 
order to illustrate certain forms of error. The condi- 
tions here should be the same as in the case of the awful 
example. Traps should never be set unless there is an 
objective standard to which the wrong answer may 
be referred. These traps are legitimate only in those 
cases in which matters can be so arranged that not only 
shall the expected mistake occur, but it shall bring its 
own condemnation with it by confronting itself with 
some irreconcilable ideas that make investigation and 



222 EXPOSITION AND ILLUSTRATION IN TEACHING 

consequent reconstruction inevitable. It may be con- 
ceded that so long as a mistake-trap leads the mis- 
take maker to perceive and rectify his mistake, no harm 
is done. But it is at the best a dangerous form of exer- 
cise, and when used should always be followed by a series 
of exercises leading to normal results, so that the final 
impression left on the pupiFs mind is the correct one. 

It is a favourite charge against the average teacher 
that he is too fond of rules. But, after all, in his mind 
the rule occupies only the second place. His real first 
love is the exception. All his professional activities 
seem to centre round exceptions. His pupils, indeed, 
acquire from the teacher's bias a distorted view of the 
relative values of rule and exception. The following 
dialogue from real life is full of instruction : — 

Teacher (going over examination paper of pupil — subject, 
French Accidence). I see you have given generals as the plural 
of general. Don't you know that nouns in -al form their plural in 
-aux'i 

Pupil. Yes, sir, but I thought it was an exception. 

Teacher. But what made you think it was an exception ? 

Pupil. Because it was set in the examination, sir. 

To the same effect is the advice given by the Scotch 
Dominie to the promising pupil whom he is sending 
up to the Scholarship Competition at Edinburgh Uni- 
versity: — 

''When in doubt mind [remember] that practically 
everything in an examination governs the subjunc- 
tive.'^ ' 

No doubt the demands of examinations have had a 
great deal to do with the unhealthy prominence given 
to exceptions. Examiners who are more anxious to 

^ Ian Hay : The Right Stuff, p. 6. 



ORDER OF PRESENTATION 223 

show what a candidate does not know than to find out 
what he does, have naturally a warm side to exceptions. 
But the teacher, too, is not without guilt. His besetting 
virtue is accuracy, and he cannot bear that even for a 
time his pupil should be told something that will not 
bear the fullest investigation. No sooner has he enun- 
ciated a general principle than some wretched excep- 
tion occurs to his mind, and he proceeds with indecent 
haste to modify his original statement by indicating in 
what respect it comes short of absolute truth as known 
to him. Before the rule has time to be established, its 
authority is undermined. The old Latin grammars 
were grossly disloyal to their rules. In a couple of lines 
they describe the behaviour of nine-tenths of the words 
under a particular category, and then having eased their 
conscience and having got rid of the herd of common- 
place words, they proceed to the real business of life and 
wallow in exceptions. The exceptions have, of course, 
a place in teaching. Fine scholarship is determined, 
no doubt, just by the accuracy with which the excep- 
tion is treated. But in a procession, mere precedence 
does not determine the importance of the people. In 
some processions the important persons come first, in 
others last, in the majority the important place is some- 
where in the middle. It does not, therefore, degrade the 
exception to say that its place is at the tail of the pro- 
cession. The rule must be thoroughly well established 
before the exception can come into being. We may in 
certain forms of teaching pass from the example to the 
rule. But we cannot pass from the exception to the 
rule. For if we try to do so, what happens is that we for 
the time being erect the exception into a rule, and then 
bring in the rule as an exception. 



224 EXPOSITION AND ILLUSTRATION IN TEACHING 

The true order of presentation is first of all to enun- 
ciate the rule, then to support it. The rule may be 
either given, as in deductive teaching, or worked for, 
as in inductive. In either case it must be buttressed 
up with many examples, and not weakened by any 
exceptions. In the case of inductive teaching the rule 
is really built up on examples. In deductive teaching 
it is justified by the examples adduced. The rule should 
be appUed in many ways, all involving normal examples 
of its working. By and by the pupil acquires confi- 
dence in his rule, and treats it as a part of the nature 
of things. Then the teacher may either introduce an 
exception, or merely permit his vigilance in editing 
examples to relax, and allow an exception to occur in 
the ordinary course of study. Whether the exception 
occurs by accident or is deliberately introduced by the 
teacher, the detection of the exception should be left to 
the pupil. Unless the pupil is struck by the exception, 
as an exception, the rule has not been properly assimi- 
lated. When the pupil comes to complain about the 
rule failing in a particular case, he is in a position to be 
told of the nature and number of the exceptions for 
which he must be prepared. It will be noted that the 
pupil's complaint in the first instance will not be against 
the rule, but against the exception. His first attitude is 
and ought to be to regard the exception as a blunder on 
the part of some one or other. 

Obviously there are cases, especially in dealing with 
older pupils, when it may be permissible to introduce 
rule and exception together. This is especially true 
when the rule has been reached by an examination of a 
great series of examples, and when the number of excep- 
tions is limited. Suppose the pupil has, after much 



ORDER OF PRESENTATION 225 

turning up of the dictionary, come to the conclusion 
that most German substantives that are dissyllabic 
and that end in e are feminine, it is desirable to add 
on the spot the limitation ^^not denoting members of 
the male sex,'^ and to give the exceptions das Auge, 
das EndCy and das Erbe. On the other hand, the ten 
German substantives now ending in e but etymologi- 
cally ending in n should be left to be discovered, as 
exceptions to this rule, and as examples of a rule of 
their own. 

So far we have been dealing with Exposition as it 
affects the individual mind. The problem is to some 
extent complicated when we treat of exposition to a 
class. The same principles of presentation must, of 
course, hold in both cases, but they may have to be 
differently applied. To begin with, when there are 
from twenty to sixty minds to be considered (and in 
the case of public exposition often many hundreds), 
it is clear that there is greater difficulty in getting at the 
common segment of mental content. In the case of a 
class doing ordinary school work there is usually much 
less difficulty on this score than one might expect. 
The ground has already been prepared. The pupils 
are of approximately the same age, they have gone 
through a similar course, they come from homes that 
are at least in a general way similar. The difficulty in 
finding common ground is mainly in connection with 
outside matters, and is felt chiefly in introducing more 
or less concrete illustrations. With a really large audi- 
ence the expositor must adopt the purely human atti- 
tude. He must assume in his hearers only the most 
universal qualities of human nature, and whatever de- 
gree of knowledge his acquaintance with the circum- 



226 EXPOSITION AND ILLUSTRATION IN TEACHING 

stances of his audience may warrant him in assuming 
as a minimum. 

In dealing with a particular mind, we may approach 
it on one particular side because we know that to be the 
most accessible. The visual and the audile, for example, 
would be approached in a different way; but with a class 
we have to make an appeal that will meet all needs. 
We may have to approach a subject from several differ- 
ent points in turn, in order that one or other of our 
approaches may appeal to the different members of 
the class. We may, for instance, present the matter 
from five different points of view. It is probable that 
some of the really capable pupils will appreciate all the 
five presentations. Others may appreciate only four 
or three or two or one. It may chance that after all 
there may be one or two in the class who have been im- 
pervious to all five modes of approach. These zeros 
may be safely regarded as unfit for class instruction, 
and as they require individual treatment maybe neg- 
lected in our present consideration. 

With regard to the others there is the serious problem 
of interest. Especially if the subject is not in itself 
difficult, it becomes very tiresome to a clever boy to 
have it explained in four different ways, after he has 
mastered it at the first exposition. The same holds of 
the other pupils for all the explanations given after 
they have mastered the point at issue. The expositor to 
a class must therefore lay his account with this danger, 
and do what he can to introduce a second line of inter- 
est that may compensate the quicker pupils for their 
enforced retreading of the old ground. It has to be 
remembered that interest does not arise merely in the 
new or merely in the old, but in the new in an old setting 



ORDER OF PRESENTATION 227 

or the old in a new setting. By the conditions of the 
case the five presentations are made from different 
points of view, and therefore fulfil to some extent at 
least the conditions on which interest depends. But in 
the actual process of teaching it is possible to introduce 
different lines of interest. The quicker pupils may be 
taken into the teacher's confidence in the recapitula- 
tory presentations. Questions that the duller pupils 
cannot answer because they have not yet caught the 
essential point may be answered by the quicker pupils 
to their own satisfaction and to the edification of the 
duller pupils. What is a line of investigation and 
discovery for the duller pupils may well be a course of 
practical applications for those who have mastered the 
principles at the first or at any rate at one of the earlier 
stages. 



CHAPTER IX 
Exemplification and Analogy 

Natueally Illustration must observe the fundamen- 
tal principle of proceeding from the known to the 
unknown. We must approach the little known by 
means of the better known, and this principle must over- 
ride all others. Probably the most fundamental mode 
of Illustration is exemplification, and this is commonly 
understood to mean the illustration of the rule by the 
presentation of examples. It would seem to be implied 
that this form of illustration always proceeds deduc- 
tively. But while in Exposition we may be said to 
pass from the rule to the example, in Illustration it 
would seem that we are really passing from the 
example to the rule. Of the two the example is 
supposed to be better known than the rule, on which 
as a matter of fact it casts light. When we say, '^ Will 
in the first person promises or threatens, and in the 
second and third persons simply foretells: as, / will go 
in spite of all he says. He will come to supper to-night, " 
we take it for granted that the person we are speaking 
to knows the shades of meaning of will in the two ex- 
amples as a mere matter of experience of the language, 
though we do not assume that he knows anything about 
the grammatical statement of the fact. 

But in practice the example may be just as well illus- 
trated by the rule as the rule by the example. Every- 

228 



EXEMPLIFICATION AND ANALOGY 229 

thing depends upon which is better known to the per- 
son we are dealing with. It is commoner, no doubt, in 
ordinary teaching to set forth a general rule and then 
follow with more or less copious examples. But it is 
quite as useful to explain a puzzling instance by refer- 
ring it to the class to which it belongs, in other words by 
referring it to the rule of which it is an example. When 
a boy on the classical side cannot understand the mean- 
ing of the word profaner in the line, 

"Where no profaner eye may look," 

the master may make matters quite clear by merely 
uttering the words ^^ Latin comparative.'' What he 
has done is to refer this troublesome example to a rule 
that he knows is familiar to the pupil. When a less 
experienced doctor calls in a more experienced one to 
diagnose a difficult case, the mere mention of the dis- 
ease by the older practitioner settles the matter by 
referring the case to the rule of which it is an example. 
Every time that the teacher suggests the particular 
geometrical proposition that will solve a ''rider," he is 
really illustrating the example by the rule. 

When we are told in the dictionary that Illustration 
means explaining or exemplifying as by means of figures, 
comparisons, and examples, it would seem that we have 
a twofold classification of the materials of Illustration. 
On the one hand there are comparisons implying like- 
ness and unlikeness, and on the other there are mere 
examples that owe their power as illustrations to the 
fact that they show some rule in operation. But 
after all, the very fact that the different examples illus- 
trate the same rule proves that they have something 
in common, and that therefore the idea of resemblance 



230 EXPOSITION AND ILLUSTRATION IN TEACHING 

is present in them also. Aristotle distinguishes be- 
tween them, calling reasoning by example paradigm 
and reasoning by resemblance analogy. In paradigm 
we reason from one example to another; but in analogy 
we reason from a more clearly stated resemblance. 
With Aristotle analogy is treated as equivalent to 
mathematical proportion, which involves the equality 
of ratios. 

Our whole experience is intelligible only on the as- 
sumption that the operations of mind and matter are 
regulated according to certain laws that act uniformly. 
The law remains the same though the cases of its appli- 
cation vary as to what may be called content. When 
therefore we find a particular law acting in connection 
with one content we assume that the same law will 
hold under similar conditions in connection with another 
content. The selection of the common element from 
two disparate cases is ^ naturally very difficult. For pur- 
poses of illustration, therefore, it is well to adopt the 
Aristotelian view of analogy as limited to the equality 
of ratios. This enables us to express all illustrative 
analogies in mathematical terms, as thus, a :h : :c : d. 
Now if a has the same relation to h that c has to <i, and 
the pupil knows either the relation that a has to h or the 
relation that c has to d, the teacher is in a position to 
illustrate the unknown relation by a reference to the 
known. In the case in which the pupil knows both of 
the relations, the teacher is still able to use the analogy 
as an illustration, but in this case the purpose will be 

1 Cf. F. H. Bradley: "The real axiom of identity is this: What is 
true in one context is true in another ; or, If any truth is stated so that a 
change in events will make it false, then it is not a genuine truth at 
all." — The Principles of Logic, p. 133. 



EXEMPLIFICATION AND ANALOGY 231 

rather the aesthetic satisfaction of the pupil than the 
clarifying of his ideas. 

In ordinary life all that great series of shorthand 
thinking that is represented by proverbial philosophy 
is based upon the assumption that metaphor does 
carry a certain amount of weight as argument. '^ You 
cannot make a silk purse out of a sow^s ear'^ may have 
no direct connection with the case of the nobleman 
who marries his kitchenmaid; but the plain man is 
satisfied that when he has quoted the proverb he has 
said something to the point in this connection. He 
feels that he has at least made matters clearer, has 
thrown light upon the subject, has illustrated it. 

As metaphor by its very nature deals entirely with 
relations, it is obviously of the first importance in 
Illustration. It is, in fact, in all cases an instance of 
Aristotelian analogy. The proverb may be represented 
in purely mathematical form : — 

sow^s ear : silk purse : : kitchenmaid : noblewoman. 

The implication is that the relation between the sow's 
ear and the silk purse is the same as that between the 
kitchenmaid and the noblewoman ; that is, that the 
one cannot be turned into the other. As an argument, 
this metaphor is unsatisfactory, and as an illustration 
its value is mainly aesthetic. It gives satisfaction by 
stating in a very effective way what a great many peo- 
ple believe to be true. In this case it is assumed that 
we know both terms of the analogy, but in most cases 
of what may be called illustrative metaphors in teach- 
ing, one pair of terms is assumed to be better known 
than the other. We have seen that it does not matter 
which pair is known, the only important point being 



232 EXPOSITION AND ILLUSTRATION IN TEACHING 

that one pair must be better known than the other. 
When we speak of being better known, it should be un- 
derstood that we are referring to knowledge of the rela- 
tion. For a metaphor to have any illustrative value at 
all, the pupil must know all four terms as terms, though 
the true relation between one of the pairs may not 
be known by him. Naturally the less known relation 
must take its place as the illustrandum. There is this 
further point, that the person using the illustration is 
supposed to know the relationship between the terms 
in both parts of the metaphor, and to vouch for the 
resemblance of those ratios. As a method of discovery, 
analogy may not always be quite reliable, but as a 
means of illustration there is no justification for its 
ever misleading, so long as it is skilfully used. The 
source of error in teaching is quite different from that 
in discovery. 

An illustrative analogy that misleads usually does so 
through a process of spreading that is characteristic of 
all untrained minds. It is not enough that the relation 
between the two terms in the first branch of the anal- 
ogy is identical with that between the two terms in the 
second: this relation must be kept within the bounds 
of the particular analogy. The tendency of the mind 
is to supply a great many subordinate analogies, and 
to hold them as of equal importance with the original. 
In other words, the illustrative analogy is really an 
abstraction which the ordinary mind tends to make 
concrete by adding on a great number of qualities to 
each pair of terms, and insisting that a series of parallel 
analogies shall hold between the different pairs. Thus 
Professor James's figure of the stream of consciousness 
has been condemned because our thoughts do not pass 



EXEMPLIFICATION AND ANALOGY 233 

once for all through the mind, and never come back. 
The critic would substitute the figure of a cistern, be- 
cause the mind is rather a reservoir from which old 
thoughts can be drawn at will. Obviously the cistern- 
figure may be condemned in its turn, on the ground that 
our thoughts do not stagnate like the water in a cistern: 
while the ideas that we draw from the mind we do not 
throw away forever after using as we do with the water 
we have drawn from a cistern. An illustration should 
be a perfect analogy as far as it goes, but it must be 
limited to the relations that give it meaning. James's 
figure was introduced to illustrate the fact that the 
contents of consciousness have bulk: our ideas do 
not form mere series, but rather masses. This is well 
brought out by the figure of the river (James, in fact, 
goes the length of giving an illustrative section^ of the 
stream), but to carry over the details is to court error. 
One might as well object that our ideas are not wet, as 
they would necessarily be if they formed part of a river. 

The case has been epigrammatically put : ^^ If a meta- 
phor will go with you a mile, do not compel it to go with 
you twain.'' 

No doubt very elaborate analogies are sometimes 
used, and worked out in much detail. Our great alle- 
gories, for instance, give many excellent examples of 
analogy skilfully maintained for long stretches at a 
time. But in all such cases sooner or later the analogy 
breaks down, and gives an opportunity for the critic 
to find serious fault. It is here that the deliberately 
constructed illustrative story or parable calls for criti- 
cism. Such stories as Professor Drummond's Baxter^ s 
Second Innings have to be judged from two different 

^ Principles of Psychology, Vol. I, p. 279. 



234 EXPOSITION AND ILLUSTRATION IN TEACHING 

standpoints: first as works of art, secondly as more or 
less consistent analogies, with a moral purpose/ 

Teaching by metaphor, in spite of Aristotle's praise of 
that figure,^ has its dangers and must be confined to the 
essentials of the relationship to be illustrated; and in 
order to keep one metaphor within its proper bounds, 
it is desirable that it should be balanced by other meta- 
phors. The relation between mind and mental content 
may be illustrated by reference to a river, a well, a 
reservoir, a kaleidoscope, a blank sheet of note-paper, a 
stage, a dome, a photographer's plate. Each figure as 
it is used is corrected by the others, and only the really 
essential relationship is left in the reader's mind. Each 
of the figures marks a certain aspect of the truth, but 
while each emphasises its own aspect it tends to restrict 
the application of all the others to their own proper 
place. The common elements in all the figures fuse, 
while the peculiarities of each are arrested by the 
peculiarities of the others. 

This advance by means of fusion and arrest is often 
applied in dealing with ordinary school subjects. The 
symmetry of many algebraic results is thus made pat- 
ent to the pupil without the direct intervention of the 
teacher. The famihar formula (a+hy = a^ + 2 ab -{■ b^ 
may be insinuated into the pupil's mind by a series 
of actual multiplications, the letters being changed 
in each case. The purely general character of the re- 
sult soon becomes clear, and the pupil sees that it is 

* This subject receives fuller treatment in Chapter X. ' 

2 "But the greatest thing by far is to have a command of meta- 
phor. This alone cannot be imparted by another ; it is the mark of 
genius, — for to make good metaphors implies an eye for resem- 
blances."— Poetics, Vol. XXII, p. 9; S. H. Butcher's translation. 



EXEMPLIFICATION AND ANALOGY 235 

unnecessary to do the actual multiplication in order 
to reach the desired result. The analogy forces itself 
upon his notice. 

In order that a metaphor may have its full value as an 
illustration, the analogy must be completely presented 
to the mind; i.e. both pairs of terms must be given at 
the same time. Even if each pair is familiar to the 
mind dealt with, they must be presented together in 
order that they may produce their proper effect. 
Unless this is done, the metaphor presents itself not as 
an illustration but as a problem. This becomes clear 
if we take one or two examples of the illustration with- 
out indicating the illustrandum : — 

"He clasps the crag with crooked hands; 
Close to the sun in lonely lands, 
Ringed with the azure world he stands. 
The wrinkled sea beneath him crawls ; 
He watches from his mountain walls, 
And hke a thunderbolt he falls.^ " 

Till we are told that Tennyson is here dealing with the 
eagle, we experience a sense of discomfort. The natural 
effect of the personal pronoun is to suggest a human 
background for the presented ideas, and we find it diffi- 
cult to make a picture that will satisfy us by combining 
in a reasonable way all the materials supplied. So soon, 
however, as we get the key to the problem, we find a 
great deal of pleasure in tracing out the parallelism. 
Given a relation, it is not very difficult to find a parallel 
that will illustrate this relation.^ But given an illustra- 

^ A Fragment, Tennyson's Works, 1883, p. 134. 

2 Jean Paul Richter appears to take a different view in the following 
passage from the Vorschule der ^sthetik, Programm IX, Section 50 : — 
"Geht ein Dichter durch ein reifes Kornfeld spazieren: so werden 



236 EXPOSITION AND ILLUSTRATION IN TEACHING 

tion, it may be almost impossible to find the original 
relation which is to be illustrated, though when the 
relation is discovered, the beauty of the comparison 
may be easily appreciated. The mental process is dif- 
ferent in the two cases. In appreciating the compari- 
son we are dealing with perception and apperception : 
in seeking for the relation that is illustrated, we are 
dealing with discovery. In the first case we have to fol- 
low a lead that is given : in the second we have to pass 
from an effect to a cause, where many causes may lead 
to the same effect, and yet only one cause will meet the 
case in point. Take the following example of a series 
of metaphors referring to an historical character: — 

"That grand impostor, that loathsome hypocrite, that detest- 
able monster, that prodigy of the universe, that disgrace of man- 
kind, that landscape of iniquity, that sink of sin, and that com- 
pendium of baseness — " 

This has the air of being a comparatively easy case. 
It would appear that from the superlative nature of 
the figures used there could hardly be two men in the 

ihn die aufrechten und korner-armen ^Ehren leicht zu dem Gleichniss 
heben, dass sich der leere Kopf eben so aufrichte . . . aber er wird 
einige Miihe haben, fiir denselben Gedanken eines zugleich unbedeu- 
tenden und doch stolzen Menschen in den unabsehlichen Korper- 
Reihen auf den Schieferabdruck jener Blume zu treffen." But every- 
thing depends upon the state of the mental content of the person 
concerned. If the teacher asks a class what the haughtily upright 
but poorly filled ears of corn make one think of, it is quite likely that 
he will get several pupils to suggest empty-headed, pompous people, 
but by emphasising the two qualities of emptiness and stiffness he 
has really suggested the comparison. On the other hand, if he asks 
a class to find an illustration among plants of an insignificant but pom- 
pous person, not many of his pupils would suggest corn at all, but 
there would be little lack of quite suitable comparisons with other 
plants, mainly flowers. 



EXEMPLIFICATION AND ANALOGY 237 

world who could fill the part. Yet if this description is 
proposed to a class of senior pupils as a problem, it is 
astonishing how many fairly intelligent attempts may 
be made without any pupil hitting upon the truth. 
King John is often selected; Nero is a favourite sugges- 
tion; and Judas Iscariot may by many be regarded as 
a better answer than the real one. We require the 
further hint that the words are those of the stout old 
cavaher, Sir Henry Lee/ before we can apply them to 
Oliver Cromwell. 

As soon as we have found the key, we see how true the 
comparison is — from Sir Henry's point of view. But 
in the following example, from one of Charles Lamb's 
essays, we have a series of epithets that are in most cases 
wonderfully apposite. When we know the subject re- 
ferred to, we admit that at least twenty of the twenty- 
seven metaphors are admirably suited to illustrate that 
subject. Yet after reading these twenty-seven illumi- 
nating metaphors without being told the subject, most 
readers find it impossible to discover what they all refer 
to. That is to say that a given relation is illustrated 
by twenty-seven parallels — of which at least twenty 
are excellent — without making it possible for the 
average man to find out what that relation is. The 
reader probably remembers the essay in question, but 
he cannot do better than try the experiment of reading 
to his most intelligent friends (or to a class, if one is 
available) the following description, and asking them to 
say what is the subject of the first is: — 

" is the most irrelevant thing in nature — a piece of im- 
pertinent correspondency — an odious approximation — a haunting 
conscience — a preposterous shadow, lengthening in the noontide of 

^ Scott : Woodstock, Chap. XXV. 



238 EXPOSITION AND ILLUSTRATION IN TEACHING 

our prosperity — an unwelcome remembrancer — a perpetually 
recurring mortification — a drain on your purse, a more intolerable 
dun upon your pride — a drawback upon success — a rebuke to your 
rising — a stain in your blood — a blot on your 'scutcheon — a rent 
in your garment — a death's head at your banquet — Agathocles ' 
pot — a Mordecai in your gate, a Lazarus at your door — a lion in 
your path — a frog in your chamber — a fly in your ointment — a 
mote in your eye — a triumph to your enemy, an apology to your 
friends — the one thing not needful — the hail in harvest — the 
ounce of sour in a pound of sweet." 

In spite of the cumulative effect of twenty-seven 
broad hints, you will almost certainly find that your 
friends or pupils fail to arrive at the true subject. 
This looks as if Lamb's ingenious series of metaphors 
was of little value in illustrating his subject. Yet the 
moment the reader or hearer knows that this subject is 
A Poor Relation, he finds that every one of the epithets 
does something towards clearing up his ideas on the 
subject. The process of selecting from each of these 
figures the element that is common to all — the fun- 
damental relationship — is of the utmost service in 
throwing light upon the relationship. 
I ■ In his essay, Lamb mercifully begins with the subject, 
so that his epithets are read with pleasurable interest. 
Sometimes, however, a writer, but more frequently a 
speaker, deliberately uses a suppressed subject in order 
to enhance the interest of his words. This is obviously 
a special application of the principle of the vacuum, and 
if skilfully applied, the method is quite justifiable. It 
is a challenge from the speaker to his hearers, and a 
great part of the charm of the problem is the activity 
it encourages within narrow limits. As a problem it 
should be presented in such a way as not to be so diffi- 
cult as the passage from Lamb would be, if uttered in 



EXEMPLIFICATION AND ANALOGY 239 

its present form before an audience. It must be possible 
for the abler among the audience to solve the problem 
before the passage is completed. More or less broad 
hints should be given throughout, and the circum- 
stances of the case should also supply a certain guidance. 
It will be readily admitted that these hints have a ten- 
dency to help each other, so that their influence is 
cumulative, as in the parlor game of ^^ Lights" in which 
two persons begin talking round some subject that is 
not revealed to the rest of the company. The subject 
is never mentioned by name, but each person who thinks 
he has guessed it, from what he has heard of the con- 
versation, joins in and tests by the relevancy of his 
remarks whether his guess is right or wrong. Obviously 
the longer the conversation lasts the greater the chance 
of the auditors to discover the subject, but all the time 
their wits must be actively employed if they hope for 
success. 

An excellent example of this form of illustrative 
teaching is supplied by an address given by Dr. William 
Osier to medical students. The reader should experi- 
ment with himself, and note the exact point at which he 
guesses the word, and the point at which he is sure that 
his guess is right. In order to prevent the possibility 
of the reader's eye catching the actual word, it is repre- 
sented by a dash in the text, but is given in a footnote 
that will be found when the page is turned : 



THE MASTER-WORD 

" It seems a bounden duty on such an occasion to be honest and 
frank, so I propose to tell you the secret of life as I have seen the 
game played, and as I have tried to play it myself. You remember 



240 EXPOSITION AND ILLUSTRATION IN TEACHING 

in one of the Jungle Stories that when Mowgli wished to be avenged 
on the villagers, he could only get the help of Hathi and his sons by 
sending them the master-word. This I propose to give you in the 
hope, yes, in the full assurance, that some of you at least will lay 
hold upon it to your profit. Though a little one, the master-word 
looms large in meaning. It is the open-sesame to every portal, the 
great equaliser in the world, the true philosopher's stone, which 
transmutes all the base metal of humanity into gold. The stupid 
man among you it will make bright, the bright man brilliant, and 
the brilliant student steady. With the magic word in your heart 
all things are possible, and without it all study is vanity and vexa- 
tion. The miracles of hfe are with it ; the blind see by touch, the 
deaf hear with eyes, and the dumb speak with fingers. To the youth 
it brings hope, to the middle-aged, confidence, to the aged, repose. 
True balm of hurt minds, in its presence the heart of the sorrowful 
is lightened and consoled. It is directly responsible for all advances 
in medicine during the past twenty-five centuries. Laying hold 
upon it, Hippocrates made observation and science the warp and 
woof of our art. Galen so read its meaning that fifteen centuries 
stopped thinking and slept, till awakened by the 'De Fabrica' 
of Vesalius, which is the very incarnation of the master-word. 
With its inspiration Harvey gave an impulse to a larger circulation 
than he wot of, an impulse which we feel to-day. Hunter sounded 
all its heights and depths, and stands out in our history as one of 
the great exemplars of its virtue. . . . Not only has it been the 
touchstone of progress, but it is the measure of success in everyday 
life. Not a man before you but is beholden to it for his position here, 
while he who addresses you has that honour directly in consequence of 
having had it graven on his heart when he was as you are to-day. 
And the master-word is — , a little one, as I have said, but fraught 
with momentous sequences, if you can but write it on the tablets of 
your hearts, and bind it upon your foreheads." ^ 

These one-sided metaphors illustrate clearly what 
Aristotle means when, after praising the use of meta- 
phors as indicating high intelligence, he goes on to say 
that as a style made up entirely of strange or rare words 

^ ^quanimitas and Other Addresses, p. 373. 



EXEMPLIFICATION AND ANALOGY 241 

is a jargon, so a style made up entirely of metaphors 
becomes a riddle. 

"For the essence of a riddle is to express true facts under impos- 
sible combinations. Now this cannot be done by any arrangement 
of ordinary words, but by the use of metaphor it can." ^ 

There arises here an interesting application of the 
principles of the order of presentation. It is clearly 
important for the illustrator to determine whether he 
ought to begin with the illustration or the illustrandum. 
Logically, the main idea should come first and the illus- 
trative matter should follow. But it is interesting to 
observe that in actual practice the poets are rather 
fond of inverting this order. ^ ^ As " is the natural begin- 
ning of a poetical comparison, and the illustrandum is 
generally held back till the correlative ^^so^' introduces 
it. We are sometimes told that in the poet's own think- 
ing the process is reversed, but it is very probable that 
in the case of our finer poets the figure frequently 
precedes in thought as it precedes in expression.^ In 
any case it suits the poet's purpose to put the figure in 
the foreground, when he is making his presentation : — 

"Thus presented, it gives more cohesion to the poetic period, 
rouses curiosity, holds it in suspense to the end; one must get to 

1 Poetics, XXII, 2. 

2 The account of the manufacture of The Raven in E. A. Poe's 
fascinating essay on The Philosophy of Composition must be taken 
with some caution. No doubt some poems have been built up in this 
way. But they are not of very high rank. The essay is full of value 
for the didactic illustrator, but is of little use to the poet. Poe has 
the didactic instinct very strongly developed. Probably he was not 
thinking of himself when he wrote : " It is the curse of a certain order 
of mind that it can never rest satisfied with the consciousness of its 
ability to do a thing. Not even is it content with doing it. It must 
both know and show how it was done." Marginalia, XLVII. 

R 



242 EXPOSITION AND ILLUSTRATION IN TEACHING 

the second part of the period in order to understand its meaning ; 
in place of which, if one presents the principal idea at first, the 
figure coming afterwards, not being expected, will have the effect of 
a mere after-thought [hors-d'oeuvre]." ^ 

It is clear that we are here dealing with the aesthetic 
use of illustration. But when we come to the didactic 
use, we must bring the illustrandum into the first rank. 
Here the purpose is not mere enjoyment, but clear 
thinking ; not a conundrum, but an exposition. Till 
he knows what is being illustrated, the pupil cannot 
understand the illustration as illustration. Accordingly, 
he is exposed to all the temptations to set up premature 
conceptions, and will thus have to do over again all his 
thinking, as soon as he finds the real point at issue. This 
is precisely what we have seen in the previous chapter 
is to be specially avoided. No doubt in the process 
of discovery and invention we are frequently thrown 
out of our reckoning, and have to rethink our thoughts. 
But when we are being taught in the sense of having 
something expounded to us, we have a right to expect 
that we shall not be misled by the person who professes 
to be our guide. 

In teaching, it may be desirable as a general rule to 
pass from particular cases to general conclusions or prin- 
ciples. But there are cases in which it is better to start 
with a clear statement of the principle and then proceed 
to illustrate it. An excellent example of the clear state- 
ment of a principle followed by a very ingenious illus- 
tration is to be found in Part III of De Quincey's 
Essay on Style. Starting from the principle which 
he finds in Paterculus that there is a tendency of intel- 
lectual power to gather in clusters, he illustrates this 

^ Paul Souriau : La Suggestion dans V Art, p. 227. 



EXEMPLIFICATION AND ANALOGY 243 

summarily by referring to the three great periods in Eng- 
lish literature: the Elizabethan, the Queen Anne, and 
the period beginning with Cowper ; and then proceeds 
to give one of the most ingeniously manipulated illus- 
trations to be found anywhere. The two great clusters 
of Greek intellect centre each round one man ; the first 
round Pericles, the second round Alexander of Macedon. 
''On good reasons, not called for in this place," he tells 
us that the year 444 B.C. is the most suitable locus 
for Pericles, while the annus mirabilis of Alexander's 
life was the year 333 b.c. The Pericles cluster is thus 
described : — 

"First come the three men, divini spiritus, under a heavenly 
afflatus, iEschylus, Sophocles, Euripides, the creators of Tragedy 
out of a village mummery ; next comes Aristophanes, who breathed 
the breath of life into Comedy ; then comes the great philosopher, 
Anaxagoras, who first theorised successfully upon man and the 
world. Next come, whether great or not, the still more famous 
philosophers, Socrates, Plato, Xenophon ; then comes, leaning upon 
Pericles as sometimes Pericles leaned upon him, the divine artist 
Phidias ; and behind this immortal man walk Herodotus and Thu- 
cydides." 

The Alexandrine cluster is not quite so brilliant, but 
De Quincey makes capital play with the two central 
figures, Aristotle and Demosthenes. Next comes Lysip- 
pus, the sculptor, and Apelles, the painter. No other 
names are mentioned : a testimonial to De Quincey's 
honesty. Names could be easily given, but as they do 
not stand for men of quite the same rank as the men of 
the Periclean cluster, we are merely told that ^Hhere are 
now exquisite masters of the more refined comedy," 
and ^'historians there are now as in that former age." 
Pericles is well balanced by '^ Alexander himself, with a 



244 EXPOSITION AND ILLUSTRATION IN TEACHING 

glittering cortege of general officers well qualified to 
wear the crowns which they will win.'' 

Having now got his two clusters, De Quincey pro- 
ceeds to unite them under the figure of the two balls of 
a dumb-bell, the cylindrical bar joining them being 
represented by the orator Isocrates, pater eloquentice 
and communis magister oratorum, Milton's ^Hhat old 
man eloquent" who, thanks to weak lungs and con- 
stitutional cowardice, contrived to keep out of trouble 
long enough to have a personal acquaintance with the 
great men of both clusters. The aged orator had seen 
twenty-four Olympiads, and therefore quite satisfac- 
torily bridged the 111 years that separated 444 B.C. 
from 333 B.C. It would be difficult to find a more in- 
genious and — perhaps with the exception of that sup- 
pressed reason for the choice of the date 444 b.c. — 
a fairer illustration of Paterculus's thesis. Every ex- 
perienced teacher will appreciate its practical value. 

While a material illustration like that of the dumb- 
bell is frequently very effective in such a connection as 
that in which De Quincey uses it, we get greater help 
from it when we keep to the region of the material. 
There it has a compelling power that it lacks in more 
abstract connections. It would require a very great 
deal of writing to convey the same accurate effect as 
is produced by the following illustration : — 

"The battle was fought as though the British troops were travel- 
ling along the radii of a fan, of which the French constituted the 
outer circumference. As the fight progressed, the fan commenced 
to contracti" 

There is, unfortunately, an ambiguity involved in the 
one word contract. As a matter of experiment with an 
intelligent class of students (age 21-24) I found that 



EXEMPLIFICATION AND ANALOGY 245 

about a third regarded the figure as implying that the 
fan began to get smaller from tip to circumference, or, 
in other words, by the diminution in the length of the 
radii. The substitution of the word close for con- 
tract removes all possibility of misunderstanding the 
expositor's meaning. A figure like this is a sort of un- 
drawn diagram. A few lines on a blackboard would 
make the matter equally clear, but in cases where a 
certain shape (in this case, the fan) is fixed in the minds 
of the pupils, it is quite legitimate to use that as a 
standard. For example, in describing the position of 
the British forces in Natal at the beginning of the Boer 
War, a newspaper correspondent asked his readers to 
treat the mountain system as a giant letter A, with the 
apex pointing north. Then he proceeded to give the 
position of Ladysmith and other towns within the letter, 
using such terms as the bridge of the A, the left leg 
of the A, the enclosed triangle of the A. These figures 
have a compelling power that directs the mind of the 
pupil, whether he will or no. 

On the other hand, such figures must be very definitely 
presented. I have seen considerable confusion arise 
in a junior class from the statement that the watershed 
of England was shaped like the letter T, since the 
teacher had to explain that first of all the top of the T 
was not quite straight, but somewhat squinted; and 
further, that the top of the T was at the bottom of the 
map. In fact, the T was standing on its head. The 
same illustration succeeded much better in another case, 
where the teacher began at once by saying that the 
watershed was like a capital T turned upside down. 
The minor differences were introduced when the pupils 
were familiar with the figure as a whole. 



246 EXPOSITION AND ILLUSTRATION IN TEACHING 

It often happens that when a generahsation has been 
stated the pupil understands it in a broad way, but is 
not quite sure as to its application. If the generahsa- 
tion is followed by one or two examples, the pupil has 
the opportunity of testing how far his impressions are 
right. Sometimes the examples show him that he has 
taken up a wrong view of the meaning of the rule, but 
even when he has not to change his first view, he feels 
a great increase in confidence from having seen the 
rule in action. A capital instance of such a useful illus- 
tration is to be found in the continuation of a passage 
quoted from Herbert Spencer in Chapter III of this 
book. If the reader will turn to the passage referred to 
and reread it,^ he will find that the following passage 
adds considerably to the clearness of the otherwise very 
satisfactory exposition : — 

"Under a clear sky, and with no trees, hedges, houses, or other 
objects at hand, shadow's are of a pure blue. During a red sunset, 
mixture of the yellow light from the upper part of the western sky, 
with the blue light from the eastern sky, produces green shadows. 
Go near to a gas lamp on a moonhght night, and a pencil placed at 
right angles to a piece of paper will be found to cast a purple blue 
shadow and a yellow shadow, produced by the gas and the moon 
respectively." 

It is now easy to admit what was suggested at the 
beginning of the chapter, that even when we are dealing 
with the most common form of illustration, the supply- 
ing of an example to make clear the application of a rule, 
we are still working within the realms of analogy. 
The example owes its value to the fact that it is in at 
least one point like all other examples of the principle 
it exemplifies; any example of the working of a rule 

' p. 76. 



EXEMPLIFICATION AND ANALOGY 247 

embodies the essential relation implied in that rule, 
however different the terms between which the relation 
exists. 

When we deal with the type as illustration, we have a 
special case of the illustration of the rule by example. 
It may be maintained not unreasonably that the type 
really combines in itself the rule and the example: 
it may be said to be a definition become concrete. It 
corresponds to all that is essential in the rule. Sup- 
pose we are dealing with insects, for instance; any in- 
sect will serve for a mere example. But only certain 
insects possess all the essential elements that go to 
the formation of the complete connotation of 'insect." 
No insect is, as a matter of fact, a perfect type of the 
class, but the cockchafer is usually selected because 
he combines all the essential qualities, though some of 
them are present only in a rudimentary form. Some- 
times it sounds inappropriate to speak of a type at all. 
Red is no more a typical colour than is any other. It 
would be difficult to quote a typical sentence. '^What 
is nobler than to die for one's country ?'' has no more 
right to be regarded as a type than has the homely 
'^Cows eat grass." But when we come to special kinds 
of sentences, — exclamatory, interrogative, declaratory, 
— we may well have a type. Having defined a loose 
and a periodic sentence, it is quite easy to select a 
sentence that is typically loose, and another that is 
typically periodic. 

In dealing with the type it is well to make it as ab- 
stract as the conditions of the case admit. The typi- 
cal insect must have a particular colour, since we cannot 
have a real tangible insect without colour of some sort. 
But of this colour abstraction should be made in ap- 



248 EXPOSITION AND ILLUSTRATION IN TEACHING 

plying our type as illustration; and as colour is one of 
the most attractive qualities, we may find this abstrac- 
tion difficult. On the other hand, in dealing with the 
various kinds of sentences, we find it easier to be 
abstract. ^'That a is b, that c is d, that e is f, that g is 
h cannot be questioned" is a typical periodic sentence. 
^^He denied that s is t, that u is v, that w is x, that 
y is z" is an equally typical loose sentence. The ad- 
vantage of expressing them in this abstract form is 
that the attention is directed to the essential point 
without being drawn off to the matter which might be 
in itself interesting. 

While the type as illustration should be made as 
abstract as possible, this abstractness should not be 
suddenly introduced. There is an important difference 
here between the beginning and the ending of a^ process 
of learning. Illustrative examples at the beginning 
of a process may be more or less concrete, with proper 
precautions against their monopolising an illegitimate 
amount of interest. When the stage of the particular 
has been mastered, the results may be well fixed in the 
pupil's mind in its barest form by means of an abstract 
type. When we are using the abstract, at any rate, it is 
well to be as abstract as possible. The introduction of 
a little of the concrete in the middle of an abstract 
formula is very disconcerting. This cannot be better 
illustrated than by reference to the abstract types of the 
periodic and loose sentences just supplied in this chapter. 
If the reader remembers — and very probably the reader 
will remember, for in actual teaching the point has 
struck quite a number of pupils — the first sentence dealt 
with the first letters of the alphabet and the second with 
the final letters of the alphabet. The pupil at once 



EXEMPLIFICATION AND ANALOGY 249 

wants to know why. He is so accustomed to find a 
meaning in all the illustrations used, and to find a 
meaning underlying the general activities of life, that 
he very naturally looks for one here. He applies the 
principle : The exception proves the rule, and wants 
to know why the matter — for in this case the bare 
letters form the matter — should be different in the two 
cases.^ Since the two kinds of sentences are regarded 
as differing merely in form, it is well to avoid even the 
trifling difference suggested by the letters. The same 
letters should be used in the two cases. As a later 
exercise, on the other hand, the examples might be 
changed, if only to show that the exact number of 
clauses and the nature of the subjects and predicates 
have nothing to do with whether a sentence is periodic 
or loose. 

^ It is because of this that in changing from Murray's Dictionary 
to Webster's in Chapter I (p. 17) I have taken the trouble to mention 
why. Had I not done so, I should certainly have been asked my 
reason by a number of readers. 



CHAPTER X 

The Story as Illustration 

When the worldly wise Chesterfield gives the ad- 
vice, '^ Never tell stories," he has in view the social 
bore. He is pleading for the rights of the individual 
in conversation, which are always endangered when 
story-telling creeps in. The teller of tales is of neces- 
sity a monopolist. 

In expository work, whether in school or on the plat- 
form, the speaker's monopoly is already granted, so 
any objection to story-telling must be based on other 
grounds. To the ordinary listener at an ordinary les- 
son or lecture, even a comparatively dull story is more 
interesting than the rest of the talking, and need 
not, if the expositor has the necessary skill, interfere 
with the development of the main line of thought. As 
a matter of fact, teaching by means of stories is of the 
most venerable antiquity and is practically universal. 
Plato recognises its importance in education. In The 
Republic ^ we have the following: — 

^^ Socrates. Shall we just carelessly allow children to hear any 
casual tales which may be devised by casual persons, and to receive 
into their minds ideas for the most part the very opposite of those 
which we should wish them to have when they are grown up ? 
" Adeimantus, We cannot. ' 

"Socrates. Then the first thing will be to establish a censorship 
of the writers of fiction, and let the censors receive any tale of fiction 

* Book II, Section 377; the English is Jowett's. 
250 



THE STORY AS ILLUSTRATION 251 

which is good, and reject the bad ; and we will desire mothers and 
nurses to tell their children the authorised ones only. Let them 
fashion the mind with such tales, even more fondly than they mould 
the body with their hands ; but most of those which are now in use 
must be discarded." 

Plato then proceeds to give examples of the sort of 
things found in the current stories of his time, in which 
the gods are represented as doing unworthy things. 
Even Homer and Hesiod are not held free from blame, 
and would require a great deal of attention from the cen- 
sor before Plato would let their works loose among 
young people. Most teachers have an uncomfortable 
feehng about specially prepared ^' books for the young/' 
and it is with a little shiver that they approve of 'Hhe 
authorised ones.'' The specially prepared story is apt 
to suffer from the dissipated interest of the author. 
He has to keep his eye so closely fixed upon the censor 
that he is apt to forget the children. 

We shall be in a better position to criticise the illus- 
trative story when we have considered its mode of 
affecting readers or hearers. There are two main pur- 
poses to be served by the story as a means of instruc- 
tion, the first limited to the communication and the 
acquirement of knowledge, the second extending to 
conduct. In the second class there are two divisions. 
For in using the story as a means of affecting conduct 
the teacher depends upon the pupil's inherent tendency 
to imitate, and according as this imitation is direct or 
mediated by some degree of reflection we have two 
forms of application, primary and secondary. There 
may thus be said to be in all three outstanding uses of 
the story. 

The first use of stories is to give practice in manipu- 



252 EXPOSITION AND ILLUSTRATION IN TEACHING 

lating ideas. Terms as presented to us in text-books are 
often inert, dead. But when we find them in use in a 
story they are living and functioning, and often explain 
their meaning by their very use in a context that is other- 
wise intelligible. We find them there as we find them in 
real life. In fact, story-reading is a kind of living at the 
second remove. It extends and enriches our experience. 
What is true about the historical novel in the teaching 
of history is true of the story in respect of life in general. 
It shows us principles in action. We know certain 
facts as facts by themselves, but in the story we find 
those facts applied in a life that is not — or at any rate 
ought not to be — very different from our own. We 
seldom realise how much we owe to stories in the way 
of education. To be sure, teachers are now rather keen 
on the subject of stories, but this modern interest is 
only the coming to consciousness of a principle that has 
been long applied. We are becoming conscious of and 
are writing about the educative influence of the old 
story-tellers, wandering minstrels, peddlers, and fireside 
Scheherazades ; but their influence has been present 
all the while. The use of the story that we are at 
present considering is independent of the moral effect 
of any deliberate lesson the story may convey. The 
value lies in the material presented to the mind for 
exercise. 

Consistency with the facts of ordinary life is surely 
a modest demand to make from the user of illustrative 
stories. The moral may be unimpeachable, and the 
rarer condition of truth to human nature may be ob- 
served, but if a glaring breach of natural law is detected 
in a story, all the rest goes for nothing: harm is done, 
not good. The classical story of the magnanimous 



THE STORY AS ILLUSTRATION 253 

miner is a case in point. The vessel is slowly settling in 
mid-ocean. The miner who is returning after having 
made his pile has completed the arrangements necessary 
to meet the catastrophe. The confiding little girl, who 
of course has no relatives on board, comes up, and in 
good Sunday-school language says, ^'Oh, sir, can you 
swim ?" He admits that he can, so she at once places 
herself under his protection, and so touched is he with 
her implicit faith [see alphabetical index] that he at 
once, though of course reluctantly, removes the belt that 
contains his gold — worth two and a half million — and 
does what is right [see under Duty in the alphabetical 
index, for the story appears under this head as well]. 
As a rule the attention is so much taken up with the 
moral side of the question that no trouble arises. But 
if anyone happens to take up the '^arithmetical chal- 
lenge^' implied in the $2,500,000, and works out the 
actual weight of this value of gold, the anecdote suffers 
serious moral damage. The weight of gold the poor 
fellow is represented as carrying in his belt weighs some 
trifle more than four tons. The pity is that the whole 
story goes to pieces on this fact, for $25,000 would 
have served the illustrator's purpose just as well. The 
smaller sum would weigh about 91 pounds, quite a 
sufficient handicap to prevent the miner trying to save 
both the girl and the belt. 

The second and most obvious use of the story is to 
incite to a definite line of action. ''Go thou and do 
likewise'' is the natural ending to stories of this kind. 
It is clear that Plato has this imitative use mainly in 
view. The doings of Uranus and Cronos are not to be 
told to the boy, lest in later years he should make a 
practical application of what he had learned and — 



254 EXPOSITION AND ILLUSTRATION IN TEACHING 

"even if he chastises his father when he does wrong, in whatever 
manner, he will only be following the example of the first and great- 
est among the gods.'' ^ 

Plato is no believer in the awful example; he knows that 
the suggestive force of imitation works in one direction 
only. This class of story, then, should be as straightfor- 
ward as possible. Parallelism should be avoided where 
direct teaching is available, and when used should be 
made as clear as possible, and as free from refinements. 
Such stories are illustrative of life, and should bear the 
test of constant comparison with things as they are. 
School stories are apt to fall lamentably short here. 
The classical sinner in this respect, if we are to believe 
the popular clamour among teachers, is Eric, or Little hy 
Little. Priggishness is the universal complaint against 
books of this class, and it is perhaps impossible to avoid 
this vice when we set ourselves deliberately to prepare 
an illustrative story. But the priggishness in moral 
school stories is trifling compared with the unnaturalness 
introduced into the Sunday-school story of commercial 
success. In business, if anywhere, it is easy to test 
recipes for success. A boy who is brought up on stories 
of the immediate commercial success that follows upon 
religious practice is apt to become unduly depressed 
when he enters on real life. In the book the young 
man is dismissed because he has lost an order by con- 
fessing that the beans were not of the same quality at 
the bottom of the barrel. This is true to life. But the 
book^ makes the employers write to the young man a 
few days later, saying they had a position of great 
trust vacant, and would he accept it at $300 increase 

1 Republic, II, 378. 

2 Bible Models, by Dr. Richard Newton, p. 57. 



THE STORY AS ILLUSTRATION 255 

on his former salary. This is not quite close to the 
facts of business life. What could be more misleading 
than the following, a type of hundreds of illustrative 
stories: — 

"A few years ago the owner of a large drug-store advertised for 
a boy. The next day the store was thronged with boys applying 
for the place. Among them was a queer-looking little fellow, accom- 
panied by his aunt. ' Can't take him/ said the gentleman ; ' he's too 
small.' 

" 'I know he's small/ said the aunt, 'but he's prompt and faithful.' 

" After some consultation the boy was set to work. [Naturally 
employers would take the smallest of the throng, if only he had an 
aunt with him.] Not long after, a call was made on the boys for 
someone to stay in the store all night. The other boys seemed 
reluctant to offer their services. But this boy promptly said, 'I'll 
stay, sir.' 

" In the middle of the night the merchant went into the store to 
see that all was right, and found the boy busy at work cutting labels. 
'What are you doing, my boy ? ' said he. ' I didn't tell you to work 
all night.' 

" 'I know you didn't, sir, but I thought I might as well be doing 
something.' 

"The next day the cashier was told to 'double that boy's wages, 
for he is prompt and industrious.' 

" Not many weeks after this, a show of wild beasts was passing 
through the streets, and naturally enough all the hands in the store 
rushed out to see them. A thief saw his opportunity, and entered by 
the back door to steal something. But this prompt boy had stayed 
behind. He seized the thief, and after a short struggle captured 
him. [Do not forget how small he was awhile ago — but then, 
maybe it was a small thief.] Not only was a robbery prevented, but 
valuable articles stolen from other stores were recovered. 

" 'Why did you stay behind,' asked the merchant of this boy, 
'when all the others went out to see the show?' 

" ' Because, sir, you told me never to leave the store when the 
others were absent ; so I thought I'd stay.' 

" Orders were given once more : ' Double that boy's wages, for he 
is not only prompt and industrious, but faithful.' [How soon one 



256 EXPOSITION AND ILLUSTRATION IN TEACHING 

acquires the doubling habit !] That boy is now getting a salary of 
twenty-five hundred dollars a year, and before long he will become a 
member of the firm. [We are a little surprised at the delay in mak- 
ing him a partner.] He was following Elijah's model of promptness, 
and it helped to make his fortune." ^ 

What a disillusionment is in store for boys brought 
up on such travesties of real life! 

The third use of the story as Illustration resembles the 
second inasmuch as it conveys a direct lesson, but differs 
from it since it does not present a simple line of conduct 
to be imitated. It rather suggests general principles 
which must be applied by the pupil to his own case. 
Sometimes it is written to order, as in the case of fables 
and allegories, but sometimes it has been made for quite 
other purposes and has had a meaning read into it by 
some ingenious expositor. New applications of famil- 
iar old stories illustrate this use. A great many of our 
political cartoons are based on this manipulation of 
old material in a new connection. An ingenious com- 
mentator illustrated his whimsical view of what he 
called ^'The Devil's Apprenticeship" by showing the 
gradual improvement in temptation methods, as shown 
by three historical examples of Satan's workmanship. 
In the case of Job he knew so little about his business 
that he endeavoured to obtain his ends by blundering 
brutality and cruelty. When it came to the temptation 
of Our Lord he had learnt enough to go about the 
matter in quite a different way; and had he had to deal 
with an ordinary case he would probably have won, 
thanks to his more attractive methods. But when the 
turn of Faust came, Satan had learned his art of tempta- 
tion so well that he was irresistible. He had learned not 

» Dr. Richard Newton : Bible Models, p. 179. 



THE STORY AS ILLUSTRATION 257 

to bully and torture; he had given up even the attrac- 
tive lure; he did not pester Faust one way or the other: 
he waited till he was called. Had the commentator 
known of the newer psychology, he might have expressed 
his meaning by saying that Satan had attained the 
point of carrying on temptation by means of pseudo- 
auto-suggestion. 

Nowhere can we find a better example of what Plato 
would call '^authorised tales" than in the Fables of La 
Fontaine. These were, and to some extent still are, 
recognised as specially suitable for the instruction of 
the young. They held the place in France that the 
Catechism held in Scotland. Children were asked if 
they knew their fables just as a teacher might ask a boy 
if he knew ''his tables, '^ or as Roger Ascham might have 
asked him if he knew "his noun." It was only there- 
fore to be expected that Rousseau would have something 
very serious to say against them. His attack in the 
Entile ^ follows two different lines, the cognitive and the 
moral. The first part of his criticism deals with the 
matter of the fables mainly from the point of view of 
the children's intelligence. He is anxious to show, in the 
first place, that children cannot understand the fables. 
When he has demonstrated this to his satisfaction, he 
proceeds to show that even if they did understand, they 
would be sure to misapply their knowledge. The first 
part, therefore, deals with the expository side, the second 
more directly with the illustrative. As both are of the 
greatest interest in connection with our subject, the 
passage is worth quoting in its entirety. Since the Rous- 
seau criticism demands a line-for-line translation of the 
fable of the Fox and the Crow, I have been driven, 

' iSdition de Ch. Lahure, 1856, Livre II, p, 490 fiF. 
s 



258 EXPOSITION AND ILLUSTRATION IN TEACHING 

though not even on speaking terms with the Muses, to 
make a rendering of my own. 

THE FOX AND THE CROW 

On tree-top perched sat Master Crow : 

Within his beak he held a cheese, 
The scent led Master Fox below, 

Who him addressed in words like these : 
" Ha ! good day, good day, dear Sir Crow ; 
How fair you are ! How do your looks me please ! 

Without a lie, if but your note 

Matches at all your beauteous coat. 
You are the phenix 'mongst the woodland train." 

These words with joy nigh turned the crow's weak brain : 

And to display his dulcet strain 
He opes his beak — down falls the cheese amain. 
The fox enjoyed the cheese, then said, ''Good Sir: 

Now learn that every flatterer 

Lives upon him his flatt'ries please : 
A lesson this no doubt well worth a cheese.'' 

Confounded and ashamed, the crow 
Swore, somewhat late, none else should have him so. 

Criticism by Rousseau 

On tree-top perched sat Master Crow : 

"Master." What is the meaning of this word in itself? WTiat 
does it mean before a proper name ? What meaning has it here ? 

What is a crow ? 

What is the meaning of "on tree-top perched "? We do not say 
" on tree-top perched," but " perched on a tree-top." Consequently 
we must speak of poetical inversions. We must tell what prose is 
and verse. , 

Within his beak he held a cheese, 

What cheese ? Was it Swiss, Brie, or Dutch ? If the child has 
never seen a crow, what do you gain by speaking to him of it ? If 



THE STORY AS ILLUSTRATION 259 

he has seen one, how can he imagine it holding a cheese in its beak ? 
Let us always make our illustrations agree with nature. 

The scent led Master Fox below. 

Another ''Master." But this time by good right. He is past 
Master in all the tricks of his trade. We must tell what a fox is, 
and distinguish his true nature from the conventional character 
which he has in fables. 

Led by the scent of a cheese 

This cheese, held by a crow perched upon a tree-top, must have 
had a powerful smell to be perceived by the fox in a thicket or in a 
burrow. Is it thus that you exercise your pupil in the spirit of 
well-balanced criticism which only allows itself to be imposed upon 
under suitable artistic conditions, and can discriminate between 
truth and lying in the tales of another ? 

Who him addressed in words like these : 

Words ! Foxes speak, then ? They speak the same language as 
crows ! Wise instructor, be careful. Weigh well your reply before 
making it : it means more than you think. 

^^Ha ! good day, good day, dear Sir Crow; 

Sir ! A title which the child sees turned into ridicule, even before 
he knows that it is a title of honour. Those who say Sir Crow will 
have plenty to do before they explain this Sir. 

How fair you are ! How do your looks me please I 

Padding, useless repetition. The child, seeing the same thing 
repeated in different terms, learns to speak slovenly. If you say 
that this redundancy is an art of the author, that it enters into the 
plan of the fox, who wants to appear to multiply praises with words, 
that excuse will do for me, but not for my pupil. 

Without a lie, if but your note 

Without a lie! People lie, then, sometimes. What can the 
child think if you explain to him that the fox only said "without a 
lie " because he was lying. 



260 EXPOSITION AND ILLUSTRATION IN TEACHING 

Matches at all your beauteous coat, 

Matches ! What does this word mean ? Teach the child to com- 
pare things so different as voice and plumage : you will see how he 
will understand you. 

You are the phenix 'mongsi the woodland train." 

The phenix ! What is a phenix ? Here we are all at once thrown 
into the fictions of antiquity, almost into mythology. 

The woodland train ! What figurative speech ! The flatterer 
ennobles his speech and gives it more dignity in order to render it 
more seductive. Will a child understand this delicate policy ? Does 
he ever know, can he know, what a noble or a low style is ? 

These words with joy nigh turned the crowds weak brain: 

One must have already experienced very keen passions to under- 
stand this proverbial expression. 

And to display his dulcet strain 

Do not forget that to understand this verse, and all the fable, 
the child must know what the dulcet strains of a crow are. 

He opes his beak — downfalls the cheese amain. 

This line is admirable. The very harmony makes a picture of it. 
I see a big ugly open beak; I hear the cheese faUing through the 
branches ; but beauties like these are lost on children. 

Opes.^ This word is out of ordinary use. It must be explained. 
» One must say that it is only used in verse. The child will ask why 
people speak differently in prose and in verse. What will you answer 
him? 

The fox enjoyed the cheese, then said "Good Sir : 

Here we have, then, already, goodness turned into vileness. 
Certainly the tree of knowledge is an early plant in our children's 
garden. 

* In the original this note applies to the word alleche in the third 
line from the beginning, but the general sense is not at all changed 
by transferring the remarks to the English poetical form, opes. 



THE STORY AS ILLUSTRATION 261 

Now learn that every flatterer 
General statement ; we are quite beyond our depth. 

Lives upon him his flatteries please : 
No child of ten will ever understand this line. 

A lesson this no doubt well worth a cheese." 

That is true, and the thought is very good. Yet there will be 
found very few children who can compare a lesson to a cheese, and 
who would not prefer the cheese to the lesson. We must get them to 
understand, then, that this remark is only a joke. What fine-drawn 
distinctions for children ! 

Confounded and ashamed, the crow 
Another pleonasm; but this one is unpardonable. 

Swore, somewhat late, none else should have him so. 

Swore ! What sort of blockhead is the master who dares to 
explain to a child what an oath is ? 

Here we have abundance of details, yet not so many as would be 
necessary to analyse all the ideas of this fable, and to reduce them 
to the simple and elementary ideas of which each of them is com- 
posed. But who believes that there is need of this analysis to make 
oneself understood by the young? None of us is philosopher 
enough to put himself in the place of a child. 

Now all this is ingenious, and very effectively put. 
Unfortunately, it does not stand the test of practical 
application. Rousseau has fallen into the very common 
mistake of underestimating the intelligence of a child. 
Further, he has made the mistake of specifying an age. 
Most of us would have thought his criticisms applied to 
a child of seven.^ We find that he has in view a child of 
ten. One of the teacher's chief difficulties with children 

^ In his criticism of the moral he speaks of " children of six." 



262 EXPOSITION AND ILLUSTRATION IN TEACHING 

of this age is to keep them from generalising too freely. 
Not only do children of ten easily understand the 
generalisation, ^^ every flatterer lives upon him his 
flatt'ries please/' but, unfortunately, many of them 
actually apply it. There is no difficulty whatever in 
getting a class of pupils of ten to understand this 
fable. As a matter of fact, the teacher of such a 
class will have to face a certain resentment among the 
pupils at having to deal with such childish matters. 
As to the special difficulties raised by Rousseau, they 
can be all easily overcome or postponed. It is not at all 
necessary, for example, that there should be an elabo- 
rate discussion of the nature of prose and verse. Chil- 
dren of ten know exceedingly well in a practical way 
what each is, and the time for a logical definition is not 
yet. Would anyone maintain that such a definition is 
necessary before a child can understand fully the fable 
before him ? The inversion that distresses Rousseau 
will certainly be noted by the pupil. He will feel that it 
is different from the rest of his book work, just as he 
notes that much of his book work is different from his 
spoken work. He is becoming practically acquainted 
with what inversion means; he is laying up a capital of 
experience of literary form against the day when he has 
to face the ordinary laws of rhetoric. The enquiry 
about the kind of cheese is puerile. The dilemma about 
seeing a crow is avoided by showing a picture — which, 
by the way, settles the relative size of the cheese at the 
same time. Rousseau and the naturalists may be left 
to fight it out about the fox's sense of smell. Grown-up 
people hear enough about the wonderful powers of 
animals in this way to be willing to accept La Fontaine 
at his face value, and children will certainly not suffer 



THE STORY AS ILLUSTRATION 263 

from following their example. As to the conventional 
character of the fox, there is not much that the child of 
ten brought up on ordinary schoolbooks does not know. 
The idea of a child learning to speak slovenly from 
imitating the style of La Fontaine ! 

^^ People lie, then, sometimes." The naif Rousseau 
would have us believe that a child of ten is not aware of 
this. Even an English judge would not dare to claim 
such ignorance. '^Matches'' would give very little dif- 
ficulty to a class of girls, and no class of boys of ten 
could be puzzled by the recondite statement, "If 
your singing is as fine as your coat is pretty.'^ Phenix 
must, of course, be explained; that is, we must tell the 
child what we have read in books about it. In two 
minutes the child knows as much about it as most of us 
go through life with. '^Can a child know what a noble 
and a low style is?'' Certainly, if only Rousseau will 
allow him to have examples of the noble style. The 
other he usually has thrust upon him. Does anyone 
think that a child of ten cannot discriminate between 
the style of a comic song and that of Hiawatha or one 
of Macaulay's Lays. Naturally the child cannot write 
a thesis on the distinction. '^Turned the crow's weak 
brain" seems to Rousseau a terrible strain on the chil- 
dren's intelligence. The trouble is that for this expres- 
sion the pupils I have tested have usually had too many 
equivalents. Unfortunately, they were rather of the 
'4ow style": — '^got barmy with joy," '^off his nut 
with joy," "so glad he got a slate loose"; not elegant, 
but horribly expressive of full comprehension. 

While on the score of intelligence Rousseau is over- 
anxious, and certainly overcritical, he has a strong 
case when he takes up the moral aspect : — 



264 EXPOSITION AND ILLUSTRATION IN TEACHING 

"I ask if it is to children of six that we should teach that there are 
men who flatter and lie for their profit ? One might at most teach 
them that there are mockers who make fun of little boys, and laugh 
in their sleeves at silly, boyish vanity; but the cheese spoils every- 
thing ; one teaches them not so much to drop the cheese from their 
own mouths as to make it drop from the mouth of another. Here, 
then, is my second paradox, and it is not the least important. 

" Observe children learning their fables, and you will see that when 
they are in a position to apply them they almost always do it in a 
way contrary to the intention of the author ; and that instead of 
guarding themselves against the vice of which we wish to cure or from 
which we wish to protect them, they are inclined to love the vice by 
means of which one makes profit out of the failings of others. In the 
preceding fable children laugh at the crow, but they have all a warm 
side towards the fox ; in the following fable you think you are giving 
them the grasshopper as an example — not at all, it is the ant that 
they will choose. One does not Hke to eat humble pie : they will 
always play the grand part; it is the choice of self-love, a most 
natural choice. But what a ghastly lesson for children ! The most 
hateful of all monsters would be a hard and miserly child, knowing 
what was asked of him, yet refusing. The ant does more : she 
teaches the child to chaff while refusing. 

^' In all the fables where the lion is one of the characters, since 
he is the most distinguished, the child never fails to make himself 
the lion; and when he superintends distribution, well taught by 
his model, he is most careful to seize everything. But when the 
gnat gets the better of the lion, that is another affair: then the 
child is no longer the lion, he is the gnat. He learns to kill one 
day by needle-thrusts those whom he dare not attack in a stand- 
up fight. 

" In the fable of the lean wolf and the fat dog in place of the lesson 
in moderation which is intended to be conveyed, he takes a lesson in 
licence. I shall never forget seeing a little girl weep copiously 
because she was being taught docility by means of this fable. Her 
friends could not understand the cause of her tears ; at length they 
learned. She felt galled like the dog ; she wept because she was not 
the wolf. 

" Thus, then, the moral of the first fable quoted, is for the child a 
lesson in the basest flattery ; that of the second a lesson in inhuman- 



THE STORY AS ILLUSTRATION 265 

ity; that of the third a lesson in injustice; that of the fourth a 
lesson in satire ; that of the fifth a lesson in self-sufficiency. 



"But perhaps all this moral which serves me as an objection 
against fables may furnish so many reasons for preserving them. 
We must have one moral in words and another in actions in society, 
and these two do not at all resemble each other. The one is in the 
Catechism, where folks leave it; the other is in the fables of La 
Fontaine." 

Depressing as all this sounds, it is not without 'its 
bright side. The very self-reference that Rousseau 
deplores is in itself a force that can be utilised by the 
teacher. It has to be remembered that, however this 
self-reference may be debased by the love of the lime- 
light, it is in itself an essential part of our nature. 
From what we have seen already as to the nature of 
consciousness, we are compelled to regard everything 
from our o\7n point of view. Whether we will or no, 
we must treat subjects on the assumption that we are at 
the centre of the universe. Not conceit but necessity 
makes us treat ourselves as the centre of all things. 

As for the desire for the best part in the drama of life, 
that also is natural, but must be regulated by the possi- 
bilities of the case. Experience must teach the child 
his true place in the play, and the least costly experience 
is that of the second remove, as supplied by stories. 
Knowing that the pupil will inevitably put himself 
among the dramatis personce of the story, and almost 
inevitably cast himself for the hero's part, the teacher 
knows how to arrange his material. To begin with, 
the knowledge of this self-referent tendency frees the 
teacher from the necessity for that blatant moralising 
that most of us dislike. This does not mean that the 



266 EXPOSITION AND ILLUSTRATION IN TEACHING 

teacher is not to take direct means to affect the pupil, 
but merely that he need not expound his methods and 
aims. If he arranges his materials properly, the pupil 
will inevitably do the rest. The story must be so pre- 
sented as to convey a clear lesson; the pupils must be 
left to draw the moral for themselves. In cases where 
there is a conflict of opinion, there is room for exposition 
and even exhortation. But when the story raises a clear 
issue, the pupils may well be left to settle the matter for 
themselves. 

A very effective example of the sort of self -interpret- 
ing story is to be found in the anecdote laid before a 
mixed class of boys and girls in one of the slum schools of 
London. There was no comment made by the teacher 
at the time, and it would almost appear as if even the 
circumstances under which the story was told in school 
might be left to be inferred from the story itself : — 

" Solomon did many other clever things besides finding out who 
was the true mother of the living child. When the Queen of Sheba 
came to see him, she gave him a great many puzzling things to do, 
but he did them all, and was never once caught out. One of her 
most cunning puzzles was to bring to him a dozen children, ail 
dressed exactly alike, with their hair just the same length and 
combed in the same way. Some of them were boys and some girls ; 
and the puzzle was for Solomon to say which were which. All he 
did was to order his servants to bring basins and make all the 
children wash their hands. When this was finished, he picked 
out those who had washed their hands only, but not the wrists, 
and said these were the boys. And he was right." ^ 

Unfortunately, certain stories are so ill adapted for 
their purpose that the pupil is not only left in doubt, 

* It goes without saying that my approval of the illustrative effi- 
ciency of this story does not carry with it approval of fabrication of 
Scripture incidents. 



THE STORY AS ILLUSTRATION 267 

but actually impelled to draw a totally wrong moral. 
Take the following story, intended to illustrate limng 
faith : — 

"At the Battle of Waterloo, Nathan Meyer Rothschild was in a 
shot-proof tent, with a swift horse saddled and bridled by his side. 
At sunset he peered over the battlefield, and saw our soldiers 
sweeping the French before them. 'Hurrah !' he cried, 'the house 
of Rothschild has won Waterloo ' : his house had lent the money for 
it. He sprang into the saddle, galloped all night, reached the 
shore at daybreak, bribed a fisherman to take him across the stormy 
sea, and by whipping and spurring, reached London thirty-six hours 
before anyone else. He used these hours in buying up all the 
stocks he could, and gained nearly two millions of pounds. Many on 
the battlefield besides him had perfect faith in the good news, but 
their faith was a thin, lazy thing, and did not rouse them to act at 
once. And so a faith that does not master and move you cannot 
make you rich in the goods of the soul. Real Christianity is a real 
living faith in a real living Saviour : it is a whole faith in a whole 
Saviour." ^ 

This story has clearly lost its way. It has strayed out 
of some ^^How to Succeed'' series, where it was com- 
fortably at home. What has this shot-proof stock- 
broker to do with the real Christianity of the conclud- 
ing sentence ? What can the boy learn from this story 
but to despise the soldiers whose thin, lazy faith did not 
rouse them to act at once, and make a dash for London 
to scramble for their share of those two millions of 
pounds ! In a case like this a moral is needed, as no one 
would suspect the author's meaning without it. But a 
story that really illustrates does not require a formal 
moral at the end. On the other hand, it is not unneces- 
sary to remark that there is nothing really disgraceful 
in using a moral. So strong is the objection some people 

^ Bible Object Lessons, James Nesbit & Co., London, 1891, p. 71. 



268 EXPOSITION AND ILLUSTRATION IN TEACHING 

have to this form of direct moral instruction that they 
would almost have us beUeve that there is something 
morally wrong in definitely proclaiming moral truth. 
The expression or suppression of the moral is a matter of 
psychology, not of ethics. There is no ethical objection 
to our urging people to be moral. The only objection 
that is valid is that we may be less able to gain our ends 
if we alienate the sympathy of our pupils by boring them 
with the moral which they can quite well draw for them- 
selves. The moral may be insinuated with much less 
chance of opposition at the beginning or in the course 
of the story. ^ The end is the fatal place, probably be- 
cause the interest has naturally run down just at this 
point. The formality and the inevitableness of the 
moral are also to be taken into account. It has all 
the unpleasantness of the bill that is presented after 
the feast is over.^ 

The story, as compared with the moral, represents 
example as compared with precept. There is room for 
both in teaching. Each has its special function. Not 
only does the story have behind it all the influence that 
belongs to imitation, but it has all the special force 
that comes from acting on one's own initiative. If we 
hear a story and ourselves make the necessary applica- 
tion to our own case, we feel that it is we who are teach- 
ing ourselves and not others who are teaching us. 
This is why people in high positions in ancient times 

^ In Section 50 of the Vorschule der Aesthetik, Jean Paul Richter 
says : " ... so wie die Moral aus der Fabel leichter zu Ziehen, als 
die Fabel aus der Moral. Ich wtirde daher (auch aus andern Griinden) 
die Moral vor die Fabel stellen." We have here, in fact, a special 
case of the problem of the Zielangabe. 

2 With regard to the formulation of the moral, see Chapter VI, 
p. 151. 



THE STORY AS ILLUSTRATION 269 

appear to have accepted in the form of fables lessons 
that would have cost the head of anyone who dared 
to present them in the form of precepts. A divine 
writing in favour of the use of religious anecdotes tells 
us: — 

"Even though silenced, people are not readily convinced and 
influenced by mere argument . . . narrating an instance of the 
effects of evil conduct often tells more loudly than a lecture against 
it, because men more readily imagine fallacy in our logic than 
falsehood in our narrative of incidents, especially when associated 
with the life of some noted individual." ^ 

It is not a matter of logic at all, but of psychology. 
We react differently to a lesson according as it is pre- 
sented to us by another or presented by ourselves to 
ourselves. Further, the association ^^with the life of 
some noted individual" is a dramatic touch, and has 
little enough to do with truth or morality. The story 
of Nathan Rothschild given above would lose a great 
deal of its dramatic point if it were told merely about 
''a certain financier. '^ But on the other hand, the use 
of such a well-known name leads to the very question- 
ings that Mr. Macleod would have us believe are 
avoided by attaching our story to a definite person. 
Investigators find that the Waterloo story is as false in 
fact as it is in teaching.^ 

^ Norman Islay Macleod : Moral and Religious Anecdotes, Preface. 

2 Rothschild was in London when Waterloo was fought. By means 
of a specially effective system of communication he received the news 
of the Sunday's battle by Monday night, and intimated it to Lord 
Liverpool on Tuesday morning. But as his Lordship had only a 
"thin, lazy" faith, he did not credit the news. On Tuesday afternoon 
a second of Rothschild's couriers brought by another route confirma- 
tion of the news ; but Lord Liverpool was still unconvinced ; and as a 
matter of fact it was thirty hours after this second courier had been 
interviewed that the official despatches came from Wellington him- 



270 EXPOSITION AND ILLUSTRATION IN TEACHING 

The question is sometimes asked : What are the 
quahties of a good illustrative story? It is easily- 
answered in a negative way at least : the good illustra- 
tive story must possess all the qualities that make an 
ordinary story good. With advanced classes, illustra- 
tive stories should be short and pointed — in the sense 
of having one point, not many. With young children 
it is wise to keep in view the general experience effect, 
even when the story is being used for moral ends. A 
certain lavishness is desirable in story-telling for the 
young. We are told that the Fables of La Fontaine, 
charming as they are, still fall far short of rousing the 
enthusiasm that rewards the telling of tales by writers 
infinitely inferior to the French fabulist. The explana- 
tion offered is that the fables are too concise. No 
sooner has the child warmed up to his work than the 
tale has ended. It is not so much that the child objects 
to the moral — it is well known that young children 
are themselves somewhat severe moralists, and if left 
to themselves would supply much more drastic penalties 
than the ordinary fabulist would sanction — as that he 
has hardly had time to lose himself in fable-land before 
he is rudely reawakened to the realities of life. It is in 
this way that one can account for the tolerance of, and 
even the preference for, somewhat long and, to older 
people, rather dreary stories. The child enjoys the 
sustained atmosphere of other-worldliness, and at the 
same time gains practice in dealing deliberately with 

self. Rothschild certainly operated on the stock exchange, but he was 
far from keeping his news a secret. Had Liverpool believed him at 
once, his Lordship might have had a share of the two millions. See 
an interesting article by Lucien Wolf in the Saturday Westminster 
Gazette (London) for June 26, 1909. 



THE STORY AS ILLUSTRATION 271 

the elements that make up the world of thought, 
whether regarded from the point of view of imagination 
or of reality. 

For this last reason it is particularly necessary that in 
the stage that succeeds the fairy tale the illustrative 
story should be in its details consistent with the facts 
of life. The pupil should be able to learn from the 
story in an indirect way a great many facts, and must 
not be misled by having impossibilities introduced into 
a story that is not honestly labelled ^^ marvellous.'' 

With older people, who can make the necessary 
allowances, liberties may be taken with literal truth, 
though artistic truth must be preserved. Wordsworth 
is not very happy in his proclamation at the beginning 
of The Westmoreland Girl: — 

** Seek who will delight in fable, 
I shall tell you truth." 

Everything depends on the kind of truth one has in 
view. Some clergymen will not use any story the literal 
truth of which they cannot vouch for. While this re- 
striction seriously limits their resources, it has the great 
compensating advantage that it prevents them from 
making the caricatures of real life that pass muster 
with some of their colleagues. But from the point of 
view of teaching there is nothing against invented sto- 
ries, except that they are usually very badly invented. 
Writers on the theory of fiction are fond of telling us 
that really high-class fiction is truer to life than the 
things that happen every day. But while The Strange 
Case of Dr. Jekyll and Mr. Hyde may be in one sense more 
true to life than many of the incidents recorded in our 
morning paper, it is not so well suited for certain illus- 



272 EXPOSITION AND ILLUSTRATION IN TEACHING 

trative purposes as a more matter-of-fact narrative. 
For advanced pupils Stevenson^ s story forms an ad- 
mirable illustration, since they can make abstraction of 
the supernatural elements, but in the case of young 
pupils the story is not suitable. The need for material 
accuracy in dealing with young children arises naturally 
from the fact that the story in their case has to serve 
the double function of illustrating some point of dis- 
course and at the same time providing material and 
giving opportunity for the acquiring of new experience 
of things in general. 

Children are notoriously fond of fairy tales, and yet 
they are also very exacting in their demand for truth in 
the stories told them. There is no real contradiction 
involved. Children naturally like to hear of wonderful 
things, and would at the same time like to believe that 
these wonderful things really happened. Long before 
school age the child keeps its fairy-tale world and its 
real world quite apart; and it is to real- world stories 
that the touchstone of truth is so rigorously applied. 
Fortunately, at early stages it is not difl&cult to get a 
sufficient number of incidents from the experience of the 
teacher and his immediate circle supplemented by 
what is available in the way of printed biography to 
meet the needs of the case; and at later stages the pupils 
acquire the power of detachment that enables them to 
see the truth in an incident that they are not sure ever 
did occur, but that might well have occurred. It is 
better for the teacher not to emphasise the fact that any 
particular story is true, as the main effect of such insist- 
ence is to make the children recognise that all the other 
stories are not true. 

It is difficult to say exactly what degree of real 



THE STORY AS ILLUSTRATION 273 

connection should be insisted on between the story and 
the lesson in which it occurs; for the degree of inge- 
nuity among teachers differs so much. One man may 
introduce almost any story to a class without danger of 
appearing to have dragged it in. Others are so clumsy 
that even an intrinsically suitable illustrative story has 
all the air of wondering how it came to find itself there 
at all. I have on my bookshelves several volumes of 
various sizes bearing some such title as Moral and Reli- 
gious Anecdotes. Some of them are published plain. 
They contain stories and nothing else. They are 
religious Joe Millers, and that is all. Others take 
a higher flight and classify their contents so that, if you 
wish to illustrate Spiritual Pride, or Worldly Wisdom, 
or Backbiting, or Fault-finding, all you have to do is to 
turn up the alphabetical index under the proper letter, 
and then select your story from those supplied. This 
wooden method appeals to certain minds, but it gener- 
ally results in pedantic dulness. The illustrations are 
technically right. They do illustrate the heads under 
which they are placed. The stories in themselves are 
usually at least moderately interesting; but somehow 
they seem to lose their sparkle when they are passed 
through the alphabetical sieve. A story that has entered 
the mind of the teacher without prejudice and is there 
worked up into an illustration is worth many gems 
culled from an alphabetical index. An experienced 
trainer of infant-school teachers under the London 
County Council urges young teachers never to use a 
story till they have ^4ived with it for three months.'^ 

The teacher's wisest course is to get his mind filled 
with the subject he is to teach, and then browse about 
among all manner of books, and mix with all manner 



274 EXPOSITION AND ILLUSTRATION IN TEACHING 

of men. Illustrative incidents will occur in the most 
unexpected places. It must not be forgotten that the 
mind imposes itself upon all that it deals with. If the 
mind is full of well-organised masses of ideas in connec- 
tion with a given subject, it cannot help fitting all the 
ideas that it accepts at all into the masses that domi- 
nate it at the time. 



CHAPTER XI 

Elaboration 

We have seen already that there is an important dis- 
tinction between having an idea and reahsing an idea/ 
This reaHsation may be regarded from the point of view 
of intensity or from that of compHcation. To reahse 
the idea of red we have to concentrate the consciousness 
in such a way as to reproduce as nearly as possible the 
state of consciousness that accompanies the actual sen- 
sation of red. But, on the other hand, we may realise 
the idea of church by allowing to come into the con- 
sciousness all the elements that go to form this idea. 
When Hobbes calls words ^Hhe counters of wise men,'' 
he means that we can use words as a sort of shorthand 
representation of concepts, and implies that we are 
entitled to use this shorthand only on condition that 
we are able to transcribe it into longhand whenever 
we are called upon to do so. In ordinary speech we 
use words representing such complex ideas as church, 
money, bimetallism, without at the moment of using 
the words bringing into consciousness more than an in- 
finitesimal part of what the words really imply. It is 
assumed, however, that if called upon we could set forth 
in detail all the elements that make up the complex idea 
we are dealing with. 

It is true that very often when we proceed to elabo- 

1 See p. 72 
275 



276 EXPOSITION AND ILLUSTRATION IN TEACHING 

rate the full meaning of a particular idea we find that it 
does not by any means contain all that we expected. 
We go through the world largely on the credit of a ful- 
ness of knowledge that is not there. One of the main 
purposes of the Socratic dialectic was to expose this 
ideational bankruptcy. Idea after idea was examined. 
The interlocutor was invited to elaborate it as far as 
he could ; and the result was nearly always that great 
gaps were exposed. When a pupil sits down to write an 
essay, he is really entering upon an exercise in elabora- 
tion. In fact, in the schools there is a recognised exer- 
cise under the name. The pupil is given a more or less 
pregnant sentence and is called upon to bring out all its 
impHcations. When Dr. Arnold invited his pupils to 
write on The Difference between Advantages and Merits, 
he really called upon them to allow their ideas on those 
subjects to develop themselves, and then to compare 
and contrast the results. For this development time 
must be allowed, so thinking at this level must be slow. 
There is naturally a very great gain in being able to do 
our thinking on the Hobbes credit system. If we regard 
thinking as the adapting of means to ends on the idea- 
tional plane, it follows that, if we can get at our ends 
without developing the content of each idea as it oc- 
curs, we effect a great saving. So long as we are work- 
ing below the Inference Point there is obviously no need 
to get small change for our ideas. In matters that 
fall below our Inference Point the ideas are so welded 
together in causal relations that we cannot use them 
amiss without rousing certain oppositions that at once 
come into consciousness, and raise the whole subject 
up to the Inference Point, and therefore secure the neces- 
sary investigation. Obviously, if we had to allow each 



ELABORATION 277 

idea to elaborate itself every time we used it, thinking 
would become impossible. Even at the Inference Point 
we do not require to make a complete elaboration of 
the relevant ideas : all that is necessary is that we should 
arrange them so that their potentialities shall be awak- 
ened, and raised to the intensity necessary to keep them 
in the subconscious state. When this has been accom- 
plished, all our mental content that is relevant to the 
subject under discussion is in an excited state, so that 
any attempt to make a combination inconsistent with 
existing combinations will be at once checked by the 
rising into consciousness of the relevant existing combi- 
nation and the consequent opposition to the proposed 
combination. 

It is not till we have reached the Gaping Point that 
it becomes necessary to allow every relevant idea to 
elaborate itself to its fullest extent, so as to bring into 
the arena all the elements that can by any possibility 
have anything to do with the problem. In this way 
we give the mind a chance of making the combination 
that will reduce the unorganised mass to order. 

A special kind of elaboration is that which takes the 
form of turning every sort of idea that will admit of it 
into some species of picture. Many people are unable 
to carry on their thinking at all without the aid of some 
sort of pictorial representation. The mental pro- 
cesses of such people may be compared to the little 
retail businesses conducted by petty traders, all of whose 
financial transactions are carried on by means of coins 
of small denominations. This small-change type of 
thinking is regarded with great contempt by some of 
the professional philosophers. Dr. Hutchison Stirling, 
for example, is very bitter on the subject. 



278 EXPOSITION AND ILLUSTRATION IN TEACHING 

''Now it is this association of ideas that constitutes thought to 
most of us — a bhnd, instinctive secution of a miscellaneous multi- 
tude of unverified individuals. These individuals are Vorstellungen, 
figurate conceptions — Ideas — crass, emblematic bodies of thoughts 
rather than thoughts themselves. Then the process itself, as a 
whole, is also nameable Vorstellung in general. An example 
perhaps will illustrate this. 'God might have thrown into space a 
single germ-cell from which all that we see now might have developed 
itself.' . . . What is involved in this writing is not thought but 
Vorstellung. In the quotation indeed there are mainly three Vor- 
stellungen — God, Space, and a Germ-cell. Now with these ele- 
ments the writer of this particular sentence conceives himself to 
think a beginning. To take all back to God, Space, and a single 
Germ-cell, that is enough for him and his necessities of thought ; 
that to him is to look at the thought beginning sufficiently closely. 
But all these three elements are already complete and self-dependent, 
— God, one Vorstellung, finished, ready-made, complete by itself, 
takes up a Germ-cell, another Vorstellung, finished, ready-made, 
complete by itself, and drops it into Space, a third Vorstellung 
finished, ready-made, complete by itself. This done — without 
transition, without explanation, the rest (by the way another 
Vorstellung) follows: and thus we have three elements with no 
beginning — at the same time that we have four with no transi- 
tion — but the fiat of the writer. This, then, is not thought, but an 
idle misspending of the time with empty pictures." ^ 

We need not take this diatribe too seriously. As to 
^ thinking a beginning/' Dr. Stirling is no doubt right. 
This demands the highest degree of abstraction. But 
there is a place for figurative thinking as well. A little 
further on in the Preface Dr. Stirling himself, re- 
luctantly, it is true, and within brackets, but still quite 
clearly, admits that there is another side : ^^(We shall 
see a side again where our abstractions are to be re- 
dipped in the concrete, in order to be restored to truth ; 

^ Preface to the original edition of The Secret of Hegel, p. xl (ed. 
1898). 



ELABORATION 279 

but the contradiction is only apparent)/' Even the 
playing with pictures is far from being an idle mis- 
spending of time. At certain stages and in certain sub- 
jects pictorial thinking has a useful function. Why 
need the pictures be empty ? Here is what a French 
philosopher has to say on the other side : — 

" ' Picturing is not reasoning ' [Image n'est pas raison] people some- 
times say. This is a great mistake. There is nothing more lucid, 
more enlightening [explicatif] than certain images. One is sure of 
having an idea that is truly intelligible when one is able actually 
to conceive it, that is to say, to bring it back to an intuition or a 
representation. To translate an abstract idea into images is to 
prove that it can be resolved into positive conceptions. This is to 
make it seen, touched, understood.^' ^ 

Herbert Spencer clearly believes that all our thinking 
is figurative, as may be inferred from the following 
passage: — 

"As we do not think in generals but in particulars — as, when- 
ever any class of things is referred to, we represent it to ourselves 
by calling to mind individual examples of it. . . ." ^ 

It is certainly too strong to say that we never think 
in generals, but the possibility of thinking in generals 
in no way militates against the contention of Souriau 
and Spencer that we can and do think by means of 
images. Even in the case of those who deny that they 
have any power of forming mental imagery, it is prob- 
able that imagery of some sort is present. Speaking 
of the loss among scientific men of the power of visual 
representation, Mr. Francis Galton tells us : — 

"The highest minds are probably those in which it is not lost, 
but subordinated, and is ready for use on suitable occasions. I am, 

^ Paul Souriau : La Suggestion dans VArt, p. 233. 
2 Essays, stereotyped edition, 1868, Vol. II, p. 15. 



280 EXPOSITION AND ILLUSTRATION IN TEACHING 

however, bound to say, that the missing faculty seems to be re- 
placed so serviceably by other modes of conception, chiefly, I 
believe, connected with the incipient motor sense, not of the eyeballs 
only, but of the muscles generally, that men who declare themselves 
entirely deficient in the power of seeing mental pictures can never- 
theless give life-like descriptions of what they have seen, and can 
otherwise express themselves as if they were gifted with a vivid 
visual imagination. They can also become painters of the rank of 
Royal Academicians." ^ 

There may not, therefore, be the fundamental differ- 
ence that Dr. Hutchison Stirling would have us believe 
between his thinking and that carried on by the ordi- 
nary person. For us the important point at present is 
that some kind of imagery is of the very essence of Illus- 
tration. Many people, after hearing a purely abstract 
statement of some argument, are quite at a loss till they 
have translated it into a series of pictures. Some of 
my friends in the philosophical faculty begin each new 
session with the resolve that they will approach meta- 
physics in a more concrete way. Their experience is 
that the students can understand each of the paragraphs 
by itself, but that because of the total lack of imagery 
they cannot grasp the subject of a lecture as a whole. 
The practical teacher is much more safe with an excess 
on the side of the concrete. But a caution is not per- 
haps out of place at this point. In the schoolroom 
so many caveats are entered against the abstract that 
among our younger teachers who have had some theoreti- 
cal training there is a tendency to regard the abstract 
as something in itself to be avoided. Certainly we 
must begin with the concrete. There is very general 
agreement with the formula : From the concrete to the 

^ Inquiries into Human Faculty and its Development, Everyman' s 
Library, p. 61. 



ELABORATION 281 

abstract. But after all, this places the abstract in the 
honourable position of being the goal of our teaching. 
The trammels of the concrete must be thrown off, so 
that our pupils may enter the freer medium of the 
abstract. Further, there must be no divorce be- 
tween the two. The abstract must be always capable 
of being expressed in terms of the concrete. There 
are occasions, of course, on which the introduction 
of the concrete only clogs the wheels of thought, 
but there are others in which the abstract thinker 
is saved from error by continual reference to the 
concrete. 

The element of time has, of course, to be taken into 
account. We sometimes hear such phrases as ^^with 
the swiftness of thought,'^ and some people appear to 
believe that thought takes no time at all. All thinking 
takes an appreciable time, but the kind that best de- 
serves the rank of being a standard of speed is the kind 
that does not hamper itself with images. To carry 
on a train of thought by means of imagery demands 
quite a considerable time. Still, the important question 
is whether this time is wasted or well spent. 

The struggle between the abstract and the concrete 
becomes acute in discussions concerning the teaching of 
arithmetic. Some teachers regard the abacus with 
suspicion, and look askance at all the infant school 
paraphernalia of beans and balls and bricks. They 
are afraid that children will acquire the concrete habit, 
and will go through life on the bean level of calculation. 
In the case of ^^ fingering" there is certainly a danger 
from the fatal convenience of this means of counting, 
but as a matter of fact the child soon tires of the limita- 
tions imposed by the beans and bricks, and seeks the 



282 EXPOSITION AND ILLUSTRATION IN TEACHING 

freedom of abstraction as soon as he finds that he can 
calculate without them. In arithmetic we need never 
want to get beyond the concrete in applying its prin- 
ciples. Teachers are too apt to regard arithmetic as 
something important by itself; to take the view of the 
mathematical savant who rejoiced that a certain theo- 
rem he had promulgated could not be used for anything 
practical. The truth of the matter is that arithmetic 
is only a particularly abstract way of regarding common 
things. The danger of excessive abstractness is no- 
where better illustrated than in those sections of our 
arithmetic text-books that elaborate certain rules for 
dealing with particular classes of concrete matters. 
Stocks and shares are marked off from mere percentages, 
and weird headings such as Alligation are used to keep 
certain matters in their special corner. The same sort 
of thing began in algebra text-books, but has fortunately 
had rather a set-back of late. The requirements of 
examinations made it worth the specialist's while to 
classify the sort of problems set, and we were beginning 
to have ^^ rules'' for clock problems, hare and hound 
problems, bath problems, age problems. Fortunately, 
teachers are realising that this is carrying abstraction 
too far. The rule must not be regarded as a means of 
saving all thought with regard to the matter to which 
it is to be applied. The place of the abstract is between 
the stating of the equation and its solution. It must 
begin with the concrete, and at the end it must square 
its results with the concrete. In the middle of the 
working of the problem we cannot say what relation 

——- has to the hands of a clock, but so soon as the 

io 

operator rises again to the '^answer" we are once more 



ELABORATION 283 

in the region of the concrete, and our results must 
stand the test of comparison with the concrete. 

It must not be forgotten that thinkers who are able 
to soar into the empyrean of the Hutchison Stirhng 
abstractions have gained their power of flight by- 
mastering the relevant concrete, and that the results of 
their high thinking must at least not contradict the 
concrete itself, though it need not be consistent with the 
quasi-abstract views that the less free thinkers obtain 
by the help of Vorstellungen. The teacher very often 
occupies the position of the abstract thinker who has 
reached a certain conclusion that he can help his pupil 
to reach only by the aid of certain figurate conceptions. 
The development of Vorstellungen in the mind natu- 
rally takes time, but the time is not necessarily wasted. 
From the figures the mind of the pupil may rise to a 
complete understanding of the underlying principle, and 
so secure his freedom. But while we are at the figurate 
stage it is necessary to go at an appropriate pace. 
We must hasten slowly, in order that we may get the 
full advantage of the stage at which our pupil stands. 
We must allow ideas to elaborate themselves so that the 
full content may be examined. Very often illustration 
consists of nothing else than giving complex ideas a 
chance to develop in consciousness in a natural way. 
Some pupils may be unable to understand an explana- 
tion that the majority of their class-mates have found 
to be perfectly clear. Before seeking out some new 
form of statement it is often well to see what can be 
done by getting the pupils to allow the ideas represented 
by the words used in the explanation to develop them- 
selves in their consciousness. When each of the ideas 
concerned is allowed to develop its implications, it 



284 EXPOSITION AND ILLUSTRATION IN TEACHING 

results that certain relations become manifest that 
would otherwise have remained hidden. 

Minds differ greatly in their power to give ideas a 
chance to develop their implications. Too often what 
happens when an attempt is made to allow an idea to 
unfold its meaning is that at the second or third remove 
from the surface meaning the consciousness is switched 
off into some other series of ideas connected by a more 
or less loose bond of association with the initial idea. 
What Professor Stout calls '^psychic fringes"^ have to 
be taken account of here. Each idea has its own fringe, 
and when several ideas are being developed at once there 
is a certain amount of interference caused by these 
fringes. Sometimes the struggle of the various fringes 
is so keen that further development is impossible, and 
some entirely new idea through a side association slips 
its way into the consciousness and drives out the ideas 
that have been trying to develop themselves. It is 
necessary, therefore, that the teacher should be ready 
with some help to the particular ideas he wishes to be 
allowed to develop. Sometimes, indeed, it comes about 
that the mere enumeration by the teacher of the ele- 
ments of a compound conception may be helpful to a 
certain class of mind. Many of our best writers illus- 
trate this need by the construction of their paragraphs. 
The first sentence enunciates the real substance of the 
paragraph; all the rest is an elaboration of the mean- 
ing contained in that first sentence. When Macaulay 
has said of Horace Walpole: '^The conformation of his 
mind was such that whatever was little seemed to him 
great, and whatever was great seemed to him little,'^ he 
has given us the whole substance of the paragraph that 

^ Analytical Psychology, Vol. I, p. 92 S. 



ELABORATION 285 

the sentence introduces. Yet when we turn to the elabo- 
ration of the idea as contained in the rest of the para- 
graph, we reahse that we understand it in a much fuller 
sense than we did before we had read the whole para- 
graph : — 

" . . . Serious business was a trifle to him, and trifles were his 
serious business. To chat with blue-stockings, to write Httle copies 
of compHmentary verses on little occasions, to superintend a private 
press, to preserve from natural decay the perishable topics of Rane- 
lagh and White's, to record divorces and bets. Miss Chudleigh's ab- 
surdities and George Selwyn's good sayings, to decorate a grotesque 
house with pie-crust battlements, to procure rare engravings and 
antique chimney-boards, to match odd gauntlets, to lay out a maze 
of walks within five acres of groimd, these were the grave employ- 
ments of his long hfe. From these he turned to politics as to an 
amusement. After the labours of the print-shop and the auction 
room, he unbent his mind in the House of Commons. And having 
indulged in the recreation of making laws and voting millions, 
he returned to more important pursuits, to researches after Queen 
Mary's comb, Wolsey's red hat, the pipe which Van Tromp smoked 
during his last sea-fight, and the spur which King William struck 
into the flank of Sorrel." 

Obviously the specific cases in which Walpole exempli- 
fies the weakness with which he is charged in the first 
sentence form legitimate illustrations of the theme. 
In such a case the expositor is assumed to have know- 
ledge of certain facts that may not be in the possession 
of the pupil. Sometimes elaboration takes the form of 
merely setting forth in a vivid way certain aspects of the 
original statement. This presentation does not imply 
any special knowledge on the part of the illustrator. 
Any of his readers may do the same for themselves from 
the material supplied, if only they have imagination 
enough. Sir A. Conan Doyle has an excellent passage ^ 

^ The Great Shadow, p. 6. 



286 EXPOSITION AND ILLUSTRATION IN TEACHING 

that exemplifies both these forms of elaboration. The 
narrator of the story wishes to convey an idea of what 
the Napoleonic wars really meant to England. He 
begins by a reference to his father : — 

" When he died we had been fighting with scarce a break, save 
only during two short years, for very nearly a quarter of a century. 
Think of it, you who live so quietly and peacefully now ! Babies 
who were born in the war grew to be bearded men with babies of 
their own, and still the war continued. Those who had served and 
fought in their stalwart prime grew stiff and bent, and yet the ships 
and the armies were strugghng. It was no wonder that folk came 
at last to look upon it as the natural state, and thought how queer it 
must seem to be at peace.'' 

Down to this point the author is simply working out 
in a vivid way conceptions that anyone with a keen 
appreciation of the situation could elaborate for him- 
self from the data assumed. This is a form of elabora- 
tion that is of special value in the schoolroom. The 
rest of the paragraph proceeds on the ordinary line of 
elaboration that adds new matter while illustrating the 
main point. 

"During that long time we fought the Dutch, we fought the 
Danes, we fought the Spanish, we fought the Turks, we fought the 
Americans, we fought the Monte- Videans, until it seemed that in 
this universal struggle no race was too near of kin, or too far away, to 
be drawn into the quarrel. But most of all it was the French whom 
we fought, and the man whom of all others we loathed and feared 
and admired was the great Captain who ruled them." 

There is a still easier form of elaboration that con- 
fines itself to simple Enumeration of elements that are 
implicit in the original conception, and could be supplied 
by the most ordinary listener or reader. No special 
keenness of observation, no gift of imagination, is re- 
quired. We have seen that suggestion acts instantane- 



ELABORATION 287 

ously in recalling all there is to recall of a given whole. 
The poet makes his suggestion, appeals to his reader, 
and leaves the rest to him. That is, the ordinary poet 
does this. For there is an extraordinary class of poets 
who seek to save their readers time and trouble by 
enumerating in detail all the elements that are implicit 
in the ideas suggested in a poem. Walt Whitman is a 
notorious sinner in this way. He is preeminently the 
poet of the catalogue. He wishes, for example, to 
emphasise the very common feeling that occasionally 
occurs to all of us of the variety of experiences that are 
going on at every moment of every day. Accordingly, 
he selects the probable conditions and doings of all the 
sailors of the globe. He gives a long catalogue, that 
reads like a quotation from a gazetteer, of the places 
where sailors are likely to be found, and another of the 
sort of things they are likely to be doing. The nature 
of the list may be inferred from the concluding line : — 

"Some with infectious diseases." 

Lest it should be supposed that this description is ex- 
aggerated, it may be well to quote one of the poet's 
catalogues. This time he wishes us to realise the great 
variety of things that may be made out of wood, and 
helps our jaded imagination with the following inven- 
tory:— 

"The axe leaps! 
The solid forest gives fluid utterances, 
They tumble forth, they rise and form, 
Hut, tent, landing, survey. 
Flail, plough, pick, crowbar, spade, 
Shingle, rail, prop, wainscot, jamb, lath, panel, gable, 
Citadel, ceiUng, saloon, academy, organ, exhibition-house, hbrary, 
Cornice, trelHs, pilaster, balcony, window, turret, porch, 



288 EXPOSITION AND ILLUSTRATION IN TEACHING 

Hoe, rake, pitchfork, pencil, waggon, staff, saw, jack-plane, mallet, 

wedge, rounce. 
Chair, tub, hoop, table, wicket, vane, sash, floor, 
Workbox, chest, stringed instrument, boat, frame, and what-not/' ^ 

Contrast this crude catalogue with the following 
lines in which Tennyson apostrophises the vessel that is 
bringing home the remains of his friend : — 

" I hear the noise about thy keel ; 

I hear the bell struck in the night : 
I see the cabin-window bright ; 
I see the sailor at the wheel. 

Thou bring'st the sailor to his wife. 

And traveird men from foreign lands ; 
And letters unto trembling hands ; 

And, thy dark freight, a vanished hfe." ^ 

Here the reader gets real help from the elaboration. 
After reading the lines he has a better picture of the 
whole scene than he had before. The poet has selected 
the most effective elements in the night scene. The 
^'bell struck in the night'' appeals to all, as is shown 
by the effect it produces when used on the stage, while 
the '^ cabin- window bright" is one of the most striking 
sights at sea, even though it did annoy KipHng's tramp 
captain. 

It may be said that Whitman should not be compared 
with Tennyson but with Homer, whose catalogues of 
ships and states and heroes may appear to give some 
justification to the modern maker of poetical catalogues. 
There were, however, more than merely rhetorical rea- 
sons for the appearance of these lists in Homer's pages, 
though it must be admitted that they also served rhe- 

^ Song of the Broad- Axe from Leaves of Grass. 
2 In Memoriam, X. 



ELABORATION 289 

torical ends and served them well. It is interesting to 
note that the love of lists is characteristic of primitive 
writing, and that this same love is also apparent among 
young children. Almost every successful writer for little 
children uses the artifice of elaborating in this more or 
less arithmetical way all ideas that lend themselves to 
it. Passages like the following are common in books 
for the young : — 

"Perhaps you do not believe in fairies! Ah, well, I am sorry 
for you. I believe in them, in every one of them — gnomes and 
sylphs, and fays and sprites, and elves and gobhns — yes, even in 
ouches — though some don't. There ! What do you think of that ? " ^ 

It is easy to see why young people should find a sat- 
isfaction in enumerating the content of a given idea. 
The elements have not yet had time to grow stale to the 
young mind. There is, further, the sense of power 
implied in the setting forth of the contents of the mental 
treasure-house. Nor must it be forgotten — and the 
consideration is not quite irrelevant to our present 
purpose — that the sense of rhythm involved in the 
enumeration of the elements is a source of keen satisfac- 
tion to the young, and is not without its attraction for 
the adult. The following example of illustrative enu- 
meration from Dickens exemplifies at once the charm of 
rhythm and the rhetorical value of this form of elabora- 
tion. The purpose is to throw discredit on the kind of 
training provided for elementary teachers in England. 
The method is to elaborate the mental content of what 
is assumed to be a typical elementary schoolmaster. 
The selected type is named M'Choakumchild, and 
this is how the elaboration is carried out : — 

^ Rev. J. R. Howatt : The Children's Pulpit, p. 270. 
u 



290 EXPOSITION AND ILLUSTRATION IN TEACHING 

"He and some one hundred and forty other schoolmasters had 
been lately turned at the same time, in the same factory, on the 
same principles, like so many pianoforte legs. He had been put 
through an immense variety of paces, and had answered volumes of 
head-breaking questions. Orthography, etymology, syntax, and 
prosody, biography, astronomy, geography, and general cosmog- 
raphy, the sciences of compound proportion, algebra, land-sur- 
veying and levelling, vocal music, and drawing from models 
were all at the ends of his ten chilled fingers. He had worked his 
stony way into Her Majesty's Most Honourable Privy Council's 
Schedule B, and had taken the bloom off the higher branches of 
mathematics and physical science, French, German, Latin, and 
Greek. He knew all about all the watersheds of all the world 
(whatever they are), and all the histories of all the peoples, and all 
the names of all the rivers and mountains, and all the productions, 
manners, and customs of all the countries, and all their boundaries 
and bearings on the two-and-thirty points of the compass. Ah ! 
rather overdone, M'Choakumchild. If he had only learnt a httle 
less, how infinitely better he might have taught much more." ^ 

As rhetoric this is somewhat unfair, but very, very ef- 
fective. Dickens was not an expert reporter for nothing, 
and a better example of deliberately inflated English it 
would be hard to find. It is notable that logic does not 
appear among the subjects, so the assaulted M'Choak- 
umchild is supposed to have been too busy with general 
cosmography to have had time to learn of an interest- 
ing little fallacy called the thaumatrope. At any rate, 
Dickens goes on using his material over and over again, 
as if his readers had never heard of Mr. Caudle's five- 
pound note. At the simple, yet in this case magical, 
word grammar, four of the most appalling words on the 
list collapse, while the commonplace word geography 
shrivels up nearly all that is left of the bubble. Yet 
it cannot be denied that grammar and geography 

^ Hard Times, Book I, Chap. II. 



ELABORATION 291 

do include the elements he enumerates, and so those 
subjects are made to appear by the mere process of 
elaboration, and the skilful repetition of the little word 
all, as something peculiarly pretentious and unneces- 
sary. Dickens has here a clearly defined point of view, 
and it cannot be denied that he has admirably illus- 
trated it. 

This illustrative enumeration is not to be confounded 
with that form of illustration that consists in presenting 
a great series of different complex conceptions, each of 
which has some element common to all the others. It 
is not a process of analysing out the common element in 
a number of cases and so coming to an understanding of 
the principle to be illustrated. When we heap figure 
upon figure to get the cumulative effect of recognising 
the same element in many different environments, we 
enrich the conception by demonstrating how widely 
it may be applied. When Burns gives us his series of 
figures illustrating the transitory nature of pleasures: — 

"But pleasures are like poppies spread, 
You seize the flow'r, its bloom is shed ; 
Or like the snowfalls in the river, 
A moment white — then melts for ever ; 
Or like the borealis race, 
That flit ere you can point their place ; 
Or like the rainbow's lovely form 
Evanishing amid the storm." ^ 

we feel that the work of realising these fine figures is 
thrown upon us, and that the result is an intensified 
awareness of the fleetingness of human delights. This 
is produced by the fusion of the common element in the 
different cases. The concrete setting of each of the 

» Tam o' Shanter, 59-66. 



292 EXPOSITION AND ILLUSTRATION IN TEACHING 

figures performs the same function, and these set- 
tings must therefore be regarded as falling under one 
category. Consequently they have to be treated as 
contrary ideas which arrest each other and thus leave 
the common elements free to coalesce. 

In enumeration, on the other hand, the predominant 
force at work is that of complication, though this pro- 
cess must be regarded from two points of view, accord- 
ing as we deal with the pupil's share in the work or the 
teacher's. Considered from the pupil's standpoint, 
elaboration consists in the breaking up of a complex into 
its elements. From the teacher's standpoint it consists 
in supplying a large number of elements that are im- 
plicit in the whole that is already a part of the pupil's 
mental content, though this whole is rather empty. 
When the teacher proceeds deliberately to enrich the 
content of a whole that he knows to exist in the mind of 
the pupil, it may be thought to be rather a matter of 
information than of illustration. Yet since the given 
whole is the starting-point, and the process results 
in making clearer the meaning of that whole, it may 
not unfairly be treated as a case of illustration. 

Take the case of trying to enrich the pupil's concep- 
tion of the state of affairs at any particular time in the 
history of the world. First of all, he should be invited 
to bring out all the ideas he has on the given period. 
Here the pupil allows divergent association to work. 
The given date suggests all manner of diverse things that 
come into the mind one after the other. It is now the 
teacher's business to arrange the ideas thus called up, 
and to supply other ideas that not merely enrich the 
content of the complex idea of the period, but place the 
old elements in a new light. Often all that is necessary 



ELABORATION 293 

to understand two disparate ideas is the presentation of 
a third which inevitably leads to a correlation of the 
two first. We have here a suggestion of the illus- 
trative power of the attendant circumstance. Fre- 
quently by presenting a matter in very great detail the 
teacher succeeds in illustrating it by giving so many 
starting-points for divergent association that one or 
other of them must lead to such a collocation of ideas 
as shall throw light upon the pupil's difficulties. 

Victor Hugo devotes a brilliant chapter ^ to the elabo- 
ration of the social and political conditions of Paris in 
the year 1817. Here he takes it for granted that his 
readers know the details that he sets about arranging 
into an organised whole. He enumerates the well- 
known persons who flourished at that period, and indi- 
cates what each was doing. He suggests the prevailing 
fashions of speech, thought, and dress. He adds illumi- 
nating sidelights in the way of vivid contrasts between 
promise and performance, between real and apparent, 
between the trifling and the significant. The effect of 
the chapter is that the reader feels that there was a 
living Paris in that year, and is ready to deal intelli- 
gently with any events that transpired then. Still, un- 
less one knows a good deal about the France of that 
time, one is not in a position to profit by the brilliant 
grouping of Hugo. His is a work of elaboration and 
enumeration rather than of knowledge-giving. This 
has to be kept in view in our teaching of history. There 
is a strange fallacy still somewhat prevalent regarding 
the text-books on this subject. It appears to be thought 
that the size of the text-book should vary in direct ratio 
to the size of the pupil: Big boy, big book; little boy, 

* Les Misirables, Part I, Book III, Chap. I. 



294 EXPOSITION AND ILLUSTRATION IN TEACHING 

little book; whereas the sizes should be in inverse ratio. 
The beginner in history should have a great deal of 
detail; he is preparing the material that will afterwards 
be used when he is called upon to elaborate, group, and 
classify. Teachers are now so eager to get at the essen- 
tials of history that they forget that the pupils must 
acquire a certain number of the facts of history. There 
is naturally no need to worry pupils with the old excess 
of dates and genealogical tables, but a great deal of wide 
general reading in history ought to precede the laud- 
able attempts to teach constitutional, and what may 
be described as scientific, history. 

Illustration by elaboration finds an important field in 
connection with definition in its wider sense. To give 
an idea of what Gothic architecture really is, we must 
do more than tell our pupils that it is that form of archi- 
tecture that prevailed between 1200 a.d. and 1475 a.d., 
and is marked by pointed arches, steep roofs, relatively 
large windows, and great height in proportion to the 
other dimensions. We must elaborate by calling atten- 
tion to many different specimens of this kind of archi- 
tecture, and by enumerating the different qualities of 
each so as to give content to the somewhat empty 
definition. 

Few words are more difficult to define than bourgeois. 
The following attempt ^ takes the form of elaboration, 
and is therefore well suited to illustrate this section : — 

"To call a person or an institution bourgeois is for her [Madame 
de Coulevain] the very worst degree of condemnation. ' Foreigners, ' 
she writes, ' often ask me the meaning of the term bourgeois. I find 

^ Winifred Stephens, French Moralists of To-day, 1908. Chapter on 
Pierre de Coulevain, p. 94. 



ELABORATION 295 

it very difficult to define. . . . Bourgeoisisme, like provincialism, 
is a mentalite. ... It communicates a shell-like impenetrability. 
Its characteristics are to be found in people who have received a 
superior culture, in whom are developed taste and a sense of beauty. 
It betrays itself by common ideas, extreme intolerance, bhnd obsti- 
nacy, an incapacity above all things to understand and to accord 
liberty. This mentalite creates a particular and unmistakable 
atmosphere. The peasant, the workman, the artisan are not 
bourgeois. I might name a king who is more so than many people 
born in the Rue du Sentier. Napoleon I was bourgeois. Napoleon 
III was not. Balzac, Guy de Maupassant were not bourgeois; 
Zola was. Two of our great newspapers, one of our best reviews are. 
The church of Saint Augustin is bourgeois, Saint Roch is not. The 
Com^die Frangaise, the Opera Comique, the Palais Royal are bour- 
geois; the Vaudeville, the Varietes, the Theatre Antoine, the 
cafes concerts of Montmartre are not. Among the tea-houses all 
are, with one exception. England, Italy, Spain are not bourgeoise; 
Germany is and her emperor is not.' Until this last sentence 
(thanks to Madame de Coulevain's kind explanation), we had im- 
agined ourselves beginning to understand the meaning of this 
enigmatical term ; but if the German Emperor be not bourgeois, 
then we are as far from understanding the word as ever we were." 

As a matter of teaching, Madame de Coulevain makes 
a serious mistake in the sentence, '^Its characteristics 
are to be found in people who have received a supe- 
rior culture/^ etc. No doubt the context shows that 
bourgeoisisme is to be found elsewhere than among 
people who have received a superior culture. But the 
teacher has no right to depend entirely upon contexts, 
and the pupil is in this sentence warranted in demand- 
ing the caution of an ^^even^^ placed before the words 
'4n people who have," etc. As illustration, Madame 
de Coulevain' s effort has evidently failed so far as 
Miss Stephens is concerned. The cause of the trouble 
is the necessity under which Madame de Coulevain 



296 EXPOSITION AND ILLUSTRATION IN TEACHING 

labours of being brilliant, antithetical, epigrammatic. 
It would have been quite possible for her to select 
less violent contrasts that would substantiate the 
distinctions implied in her general description of 
bourgeoisisme. 

Often elaboration may be very usefully employed 
along certain clearly defined lines. To get a clear idea 
of something, it is frequently desirable to isolate certain 
groups of ideas. It is sometimes worth while to attend 
to only one set of things for a while, to the exclusion of 
certain concomitants. For example, it might be use- 
ful to select from all the available biographies what 
certain men of a particular class of genius were en- 
gaged with at a certain fixed age, say 25. It is a capital 
exercise to make a class discover what was occupying the 
attention of ten selected poets, or generals, or states- 
men, or men of science at this age. A particularly 
interesting exercise is to make the age coincide with that 
of the pupil, and put the exercise in the form: What 
were the following distinguished men occupied with and 
interested in at your own age? The difficulty is no 
doubt to get accurate and full details of the earlier 
years of important men. But great ingenuity is often 
shown by pupils in interpreting in terms of their own 
experience the scanty materials found in biographies. 
We have here, in fact, an excellent illustration of the 
process of elaboration guided by the subjective feeling 
of the pupil. 



CHAPTER XII 

Degree in Illustration 

In a general way we must distinguish between the 
quantitative and the quahtative in Illustration. It 
may be possible to illustrate a certain fact or relation 
without having to go into quantitative details. There 
are some matters that we either understand or we do not 
understand. The meaning of such conceptions as size, 
cause, number, intensity, may be clearly conveyed and 
intelligibly illustrated in the course of ordinary exposi- 
tion, without any undue strain on the part of the pupil. 
A general knowledge of any of these conceptions may be 
gathered from a comparatively small number of cases. 
No doubt, in order to enrich the conceptions, it is neces- 
sary to multiply examples, but the nature of the con- 
ceptions does not change, however great the number of 
examples adduced. The idea of number as number, 
and of size as size, remains the same, no matter what the 
nature of the phenomena may be in connection with 
which number and size are studied. But a pupil may 
be able to understand very clearly what size and number 
are, and yet may be unable to realise the meaning of 
certain sizes and numbers. It is one thing to understand 
the general meaning of a term, it is quite another to 
appreciate intelligently the degrees that may be in- 
cluded within the scope of that term. The pupil may 
have quite a clear mastery of the meaning of number, 

297 



298 EXPOSITION AND ILLUSTRATION IN TEACHING 

and yet may have no real command over the concept of 
a milUon. In these days of milhonaires and multi- 
millionaires it may be a little easier to attach a definite 
meaning to the figures 1,000,000; and it is probable 
that Ruskin, in the following passage, underestimates the 
percentage of people who know the meaning of a million; 
but there is enough truth in it to make it worth our 
attention : — 

" In our exceeding prudence we are, at this moment, refusing 
the purchase of, perhaps, the most interesting picture by Raphael in 
the world, and certainly one of the most beautiful works ever 
produced by the art-wisdom of man, for five-and-twenty thousand 
pounds, while we are debating whether we shall not pay three 
hundred millions to the Americans, as a fine for selling a small frig- 
ate to Captain Semmes. Let me reduce these sums from thousands 
of pounds to single pounds ; you will then see the facts more clearly 
(there is not one person in a million who knows what a ' million ' 
means ; and that is one reason the nation is always ready to let its 
ministers spend a million or two in cannon, if they can show that 
they have saved twopence-haKpenny in tape). These are the facts, 
then, stating pounds for thousands of pounds; you are offered a 
' Nativity ' by Raphael, for five-and-twenty pounds, and cannot 
afford it ; but it is thought you may be bulhed into paying three 
hundred thousand pounds, for having sold a ship to Captain 
Semmes." ^ 

This method of proportionate reduction is certainly 
useful in giving an idea of relative values, but it in- 
troduces complications of its own. A Raphael at 
twenty-five pounds is as incongruous as a fine of three 
hundred millions for selling a ship. Further, when the 
reduced total still amounts to the vast sum of three 
hundred thousand pounds, it is probable that all who 
really understand this quantity would also have an 

^ The Eagle's Nest, Lecture II. 



DEGREE IN ILLUSTRATION 299 

intelligent mastery of the concept three hundred 
miUions. 

But it has to be admitted that the expositor is faced 
by serious difficulties the moment he introduces the 
notion of degree. The pupil is found to be able to use 
his conceptions only within certain limits determined 
by his range of experience. When asked as a school 
exercise to write a letter to a companion telling how he 
spent a quarter given by a generous uncle, a pupil from 
a poverty-struck home will often write intelhgently 
and interestingly. But if the teacher makes the imagi- 
nary uncle prodigal enough to present a ten-dollar bill, 
the result on the composition is disastrous. The pupil 
cannot rise to the expenditure of such a vast sum. A 
quarter is a real thing to him, a coin that he has handled, 
a sum of money that he has already manipulated, 
though perhaps never with the entirely free hand 
permitted in an irresponsible letter. He may have seen 
a ten-dollar bill, and is certainly able to tell you at a 
moment^s notice how many quarters he could get in 
exchange for it. But to the poor boy the bill is some- 
thing beyond the range of everyday operations. It 
represents capital rather than cash, and in consequence 
the letter usually takes the form of various recommenda- 
tions for banking the troublesome money, or at any rate 
making some economic or philanthropic use of it. A 
common device among young letter-writers under such 
trying circumstances is to describe the spending of, say, 
one dollar out of the whole, in ways that appeal to 
young desires, and to hand over the remaining nine to 
mother, who is so badly in need of them. A boy from a 
wealthy home, if asked to write a similar letter on a ten- 
dollar basis, finds no difficulty; but a $1000 bill gives 



300 EXPOSITION AND ILLUSTRATION IN TEACHING 

him pause. Yet while the difference between $10 and 
$1000 is greater than that between a quarter and $10, 
the wealthy boy finds less difficulty in passing from 
the small bill to the big one than his poorer fellow 
has in passing from the quarter to the small bill. 
Accustomed to copious supphes of pocket money, the 
rich boy is less impressed by $1000 than the poor boy 
by $10. 

In relation to any class of phenomena, we have all 
different thresholds of impressionability. What would 
astonish a farm-hand in New York would make no im- 
pression on a seasoned dweller in that city; while the 
New Yorker, as paying guest at a farm, finds himself 
impressed by many things that leave his hosts un- 
moved. In any department we must have stimuli of 
a certain degree of intensity before we are impressed ; 
this intensity may be increased up to a certain point, 
but when this point is reached, we pass beyond the 
upward limit of impressionability. 

For the benefit of Shadrach, Meshach, and Abednego, 
Nebuchadnezzar "spake, and commanded that they 
should heat the furnace one seven times more than it 
was wont to be heated. ^ ' ^ This passage worried me when 
I was a boy. To me a furnace was a furnace, and once 
it had been properly kindled and was well supplied with 
fuel, it was as hot as it could be. I was unable to under- 
stand how it could be hotter; and further, even if it 
could, I was at a loss to see how that was going to 
benefit Nebuchadnezzar. As soon as his three victims 
were placed in the furnace, they would be instantane- 
ously burnt up. I could not conceive of degrees of 
combustion. A man was either burnt up or he was 

^ Daniel Hi. 19. 



DEGREE IN ILLUSTRATION 301 

not. My boyish point of view I find well illustrated in 
a remark made by Mr. H. G. Wells in speaking of the 
wonders of Niagara. He is not greatly impressed, and 
says: ^^A hundred tons of water is just as stunning as 
ten million. A hundred tons of water stuns one alto- 
gether, and what more do you want ? " ^ I could not un- 
derstand what more Nebuchadnezzar wanted. My reli- 
gious instructor informed me that I need not worry 
about the number seven. The passage had no arith- 
metical signification, and merely meant that the fur- 
nace was heated very much more than usual. This 
was no doubt quite satisfactory from the religious stand- 
point, but it left something to be desired in other direc- 
tions. Indeed, it was not till I had come across certain 
figures some years later regarding the temperatures 
in blast-furnaces that I realised that there might be 
good science as well as good religion in the story found 
in Daniel. 

It is true that the figures I encountered raised fresh 
difficulties. It was stated in the text-book that at the 
mouth of a certain blast-furnace the temperature was 
320° centigrade, and that it went on increasing with the 
depth, till at a distance of 34 feet from the mouth the 
temperature was 1450° C. This enormous tempera- 
ture was clearly far beyond my Threshold of Stun. 
Between zero and 100° C. I felt that I not only under- 
stood but realised the different degrees of heat. I had 
experienced the heat of boiling water, and ordinary 
childish curiosity had given me a fleeting experience 
of the presumably higher temperature of red-hot iron. 
I was quite convinced that after the boiling point of 
water I had no clear notion of what increase in tempera- 

^ The Future in America, p. 72. 



302 EXPOSITION AND ILLUSTRATION IN TEACHING 

ture meant. It accordingly conveyed little to my mind 
when I was told that the heat at the bottom of a blast- 
furnace is so great that it must be measured by a num- 
ber fourteen and a half times as great as that which 
measures the heat of boiling water. Still, as experience 
brought me more and more examples of very high tem- 
peratures used in actual processes, I began to have a 
working knowledge of what these temperatures may 
mean. The fusing points of the different metals 
naturally supply figures that have a practical value. 
When the pupil is told that pure silver fuses at 960° C, 
pure gold at 1075° C, and pure platinum at 1775° C, 
he begins to attach a meaning to those high tempera- 
tures. If, now, he examines the table of fusion points 
of Prinsep's Alloys (the silver and gold series, and the 
gold and platinum series), he gets a still clearer view of 
the meaning of relativity of temperature. To realise 
in any degree the still higher temperature of the oxyhy- 
drogen flame (estimated by Bunsen at 2844° C.) and 
the electric arc (3000° C. to 3900 C.°), the pupil must 
familiarize himself with certain processes with which 
these are connected. 

In all this practical application, in order to acquire an 
intelligent acquaintance with matters entirely beyond 
our Threshold of Stun, it will be found that there is a 
natural tendency always present to interpret unrealis- 
able quantities in terms of realisable. For example, when 
the pupil is told the various temperatures of the differ- 
ent parts of the Bunsen flame — outer flame 1350° C, 
violet 1250° C, blue 1200° C, central dark cone from 
250° to 650° C, he finds that he has a sort of impression 
that the inner dark cone is comparatively cool. The 
very introduction of this term cool is an indication of a 



DEGREE IN ILLUSTRATION 303 

reference to a subjective instead of to an objective 
standard. This mixing of standards is to be avoided, 
except in cases in which we are working below the 
Threshold of Stun. The moment we have risen above 
that threshold we must do our comparisons in terms 
of units that may have been originally fixed in rela- 
tion to something within our subjective experience, 
but which, once we have passed the threshold, can no 
longer be tested by reference to that experience. 

Without making any pretence of severe scientific 
accuracy in this matter of stun, we may help our think- 
ing by using some of our terms in a clearly defined 
way. Let that degree of intensity of stimulus that just 
rouses our attention to a particular fact or phenomenon 
mark the Threshold of Impressionability to that class 
of facts or phenomena. All the range between this and 
the point at which we are stunned may well be spoken 
of as the Zone of Impressionability. Above the Thresh- 
old of Stun, of course, is the region where nothing mat- 
ters, so far as direct experience goes. 

In dealing with the rich and poor boy, we were practi- 
cally working all the time within the Zone of Impres- 
sionability. Neither of the boys was really stunned. 
Each of them found himself faced by a certain diflSculty 
in dealing with quantities beyond his usual scale; but 
neither was brought up against unintelligibility as 
would have been the case had they been called upon to 
deal with millions in a practical way. In the case of 
temperatures we find that there is a small range within 
which heat can be estimated by sensation, but above and 
below this range there are long sweeps of gradations of 
temperature that may be understood and intelligently 
applied, but that cannot be interpreted in terms of 



304 EXPOSITION AND ILLUSTRATION IN TEACHING 

sensation. In estimating the climate of a country or 
the heat of a bath, a writer may depend upon his readers 
making subjective references, and he knows within 
what Hmits he can depend upon not exceeding their 
Threshold of Stun. But in all temperatures above 
and below the points at which the human organism 
ceases to record gradation there is no meaning in refer- 
ring to sensations in estimating heat. There is no need 
that we should have a physical reahsation of 200° C, 
not to mention 2400° C. 

In a crude physical sense we may treat the range 
within which the bodily organism records gradations of 
temperature as 'the zone of impressionability to heat. 
But our mental impressionability to ideas of the 
gradations of heat is a quite different matter. Our 
physical Threshold of Stun is reached long before our 
mental. Even on the physical basis the Threshold of 
Stun may be slightly raised. The exact number of tons 
of water that would stun Mr. Wells at Niagara might 
not be enough to stun him at a later stage if he took to 
living close by a waterfall that carried just the requisite 
number of tons to stun him at the present moment. 
By and by it would be necessary to increase the number 
of tons if the stunning was to be kept up. But this 
raising of the threshold could not be carried very far. 
A point is soon reached beyond which the stun is in- 
surmountable, and indeed this higher degree of stimulus 
would probably lead to the permanent injury of the 
organs stimulated. 

On the mental side, however, there is nothing to 
hinder the gradual but steady raising of the Threshold of 
Stun with regard to any of the departments of the activ- 
ity of the mind. It may be said that an important part 



DEGREE IN ILLUSTRATION 305 

of a teacher's work consists in the raising of the Thresh- 
old of Stun, a Uttle on the sensational plane, and a 
great deal on the intellectual. It is his business to use 
the senses and the ideas so as to provide a basis on 
which the pupil may continue to build in such a way 
that his Threshold of Stun shall continue rising in 
those matters that are important to him. There is no 
reason for this raising process to cease till physical 
decay intervenes. 

In the matter of large numbers and vast distances, 
teachers are fully alive to the need for finding means to 
enable the pupil to realise quantities that are at first 
quite beyond him. The usual plan adopted is to in- 
stitute some sort of comparison between small and great. 
In particular the attempt is made to get rid of the unin- 
telligibility of vast numbers by expressing the results 
of some process of manipulating them. The following 
is a typical attempt to get people to realise the enor- 
mous distances dealt with in astronomy : — 

'^Let us suppose a railway to have been built between the earth 
and the fixed star Alpha Centauri. By a consideration of this rail- 
way's workings we can get some idea of the enormous distance that 
intervenes between Centaurus and us. Suppose that I should de- 
cide to take a trip on this new aerial line to the fixed star. I ask 
the ticket agent what the fare is, and he answers : — 

'' ' The fare is very low, sir. It is only a cent each hundred miles.' 

" ' And what, at that rate, will the through ticket one way cost ? ' 
I ask. 

" ^It will cost just $3,750,000,000,' he answers. 

" I pay for my ticket and board the train. We set off at a tre- 
mendous rate. 

" ' How fast ? ' I ask the brakeman, ' are you going ? ' 

" 'Sixty miles an hour, sir,' says he, * and it's a through train. 
There are no stops.' 

" 'We'll soon be there, then, shan't we ? ' I resume. 



306 EXPOSITION AND ILLUSTRATION IN TEACHING 

" 'We'll make good time, sir/ says the brakeman. 
'"And when shall we arrive ? ' 
" 'In just 48,663,000 years.' " 

— Philadelphia Bulletin} 

The enormous fare is certainly very impressive, but 
it is doubtful whether much is gained by representing 
the distance in terms of money, since in any case the 
numbers are clearly beyond the Threshold of Stun. No 
pupil can really appreciate the meaning of three and 
three-quarter billions, and if he is to be impressed by the 
mere number of digits, it would be more effective to tell 
him plainly that Alpha Centauri is 37,500,000,000,000 
miles away. As a matter of experience I found that 
many people to whom this illustration was presented at 
once proceeded to reduce the dollars to cents and then to 
multiply the result by one hundred in order to get at the 
exact number of miles. It may be felt that at any rate 
the forty-eight million years will help the pupil to realise 
the enormous distance. But the time is so great that 
there is an opportunity for the mind to conceive of the 
journey as being a rather restful experience. Instead 
of being impressed by the enormous space passed over, 
the mind is inclined to dwell upon the evenness of the 
journey. So far as the illustration appeals to the picto- 
rial, it defeats the ends of the illustrator, for the hurry 
and bustle of the train disappear when we project it 
against the silence of limitless space. 

It is interesting to compare a parallel illustration of 

^ Quoted by Mitchill and Carpenter : Exposition in Class-room Prac- 
tice, p. 231. Those who accept the arithmetical challenge and seek 
to reconcile the dollar calculation with the result in years will find 
their work cut out for them. It would appear that in cases of such 
vast numbers the arithmetical challenge is less alluring than usual. 
The reader is inclined to take the writer's word for it. 



DEGREE IN ILLUSTRATION 307 

the same distance as found in Sir Robert Ball, who is a 
master in such matters. He begins by bluntly stating 
the distance, which he says may be expressed in miles 
by a 2 followed by thirteen ciphers. Knowing that the 
expression 20,000,000,000,000 (which, by the way, does 
not correspond to the Bulletin's figures — but fortu- 
nately we are not here responsible for the facts that we 
have to illustrate) is far beyond his readers' Threshold of 
Stun, he sets about an explanation ^ that is an admirable 
illustration of the process of elaboration. Like the 
Bulletin, Sir Robert arranges for a special tariff : in his 
case a penny per hundred miles. Then taking the 
British National Debt, which at that time (April, 1887) 
amounted to £736,000,000, he seeks to make his readers 
realise this vast sum by first of all pointing out that the 
mere interest at a low rate amounts to £60,000 per day. 
Then he imagines the youngster filling his pockets 
with gold so as to go and buy a ticket. Pockets failing, 
a cart has to be called in: ten carts, fifty carts, a hun- 
dred carts. Finally, the young traveller starts at the 
head of his procession of five thousand carts of gold,^ 
only to find that, so far from getting any change back, 
he is still more than £100,000,000 short of the specially 
reduced fare. 

Approaching the matter anew from a different point, 
Sir Robert gives some figures regarding the number of 
miles of cotton yarn produced in a Lancashire mill, then 
in all the Lancashire mills. Finally, he works up to the 

^ Starland, p. 317. The book is a popular Exposition intended for 
young readers. 

2 On a calculation on the basis of 3| sovereigns to one ounce avoir- 
dupois, it would not appear that each cart was overladen. Yet 263 
pounds demand a vehicle of some sort, so the illustration may be Jus- 
tified. 



308 EXPOSITION AND ILLUSTRATION IN TEACHING 

statement that 400 years would be necessary for enough 
cotton to be grown in America and spun in England 
before there would be enough thread to reach to the 
nearest fixed star. But the highest point is reached 
when he says that '^AU the spinning that has ever yet 
been done in the world has not produced a long enough 
thread'^ to reach from the earth to the nearest fixed 
star. This spinning illustration I find causes too many 
questions to be asked as to details. Are the American 
mills included, or must all the spinning be done in 
England ? — and so forth. Illustrations should not 
challenge such queries. 

Sir Robert's illustration from the fact that from 
certain of the fixed stars, in spite of the enormous 
velocity of light, it would be possible at the present 
moment to see the Battle of Waterloo going on, is 
damaged by the pathetic condition, if the inhabitants 
''had good enough telescopes." Strangely enough, this 
if is a much greater stumbling-block to pupils than that 
in the other illustration, that if a telegraphic message 
had been sent off at the time to announce the birth of 
our Lord, it would be still on its way to some of the 
remoter fixed stars. In all this we are quite bej^ond the 
Threshold of Stun, and the materials of our illustration 
are tested more from the terrestrial than the celestial 
point of view. Somehow my students almost unani- 
mously confess to be much more impressed by the tele- 
gram illustration than by all the others, though several 
have said that they enjoyed lingering over the possibili- 
ties of what could be seen from appropriate stars. 
Here we have the illustration becoming the substantive 
matter of thought. 

The change from the railway unit to the telegraphic 



DEGREE IN ILLUSTRATION 309 

certainly increases the general impression of enormous 
distances. If we go on multiplying examples, we do 
gradually get a notion of the relativity involved. But 
the only way in which we can realise vast quantities 
is by manipulating them, and utilising the conception 
of relativity so as to reach certain practical conclusions 
respecting the matter actually involved. When the 
astronomer tells us that Sirius is 1,375,000 times farther 
away from us than the sun is, we take the gentleman's 
word for it ; but we do not realise what he means. It is 
true that some of us would accept the arithmetical 
challenge implied in his statement and work out the 
equation : — 

93,000,000 X 1,375,000 = 127,875,000,000,000 

and some of us might derive satisfaction from being 
able to say that Sirius is one hundred and twenty-seven 
trillion eight hundred and seventy-five billion miles 
from the earth; but are we any farther forward as to 
what it all means ? The answer is to be found in the 
fact that we can manipulate these figures in an intelli- 
gent way. We can make calculations and come to 
certain conclusions based on them, conclusions, be it 
observed, that a plain man can come to on his own 
account when the matter is properly presented to him. 
The following is taken from a school text-book that was 
formerly very widely used and in which a small section 
is set apart for purely astronomical matters : — 

"It has been calculated that if the sun were removed to the 
distance of Sirius, it would shine with only j\s part of its lustre, 
and it has been conjectured, therefore, that the diameter of Sirius 
must be at least twelve times greater than that of the sun. Of this, 
however, we cannot be certain, for spectrum analysis has taught us, 
among other things, that stars shine with different degrees of bright- 



310 EXPOSITION AND ILLUSTRATION IN TEACHING 

ness, owing probably to differences of temperature, and that Sirius 
is among the hottest and brightest of all." ^ 

We have here a calculation — not a very safe one, as 
the writer warns us, but quite an intelligible one — 
based upon the enormous distance that we admit we 
cannot realise. The calculation is none the less valid. 
Further, when we begin to compare one fixed star 
with another, and to arrange the stars into their various 
magnitudes, we gradually begin to attach a more or 
less definite meaning to the enormous astronomical 
numbers: we can behave intelligently towards them. 
So with the minute subdivisions implied in the atomic 
theory, and the newer theories that appear to demand 
an even minuter subdivision. Chemists can act intelli- 
gently upon certain calculations based on units that they 
cannot realise. 

The following illustration was burned into my mind 
at a very early period. It occurs in the geography 
text-book ^ on which I was brought up : — 

"The distance from Liverpool to New York is about 3500 miles, 
and can be traversed in about 10 days. At this rate the time re- 
quired to go from the Sun to the planets would be as follows : — 
289 years to Mercury. 
540 years to Venus. 
744 years to Earth. 
1,127 years to Mars. 
1,720 years to the nearer Asteroids. 
2,372 years to the more distant Asteroids. 
3,867 years to Jupiter. 
7,092 years to Saturn. 
14,262 years to Uranus. 
22,521 years to Neptune. 
156,500,000 years to nearest fixed star. 

^ William Lawson : Outlines of Physiography, p. 249. 

2 Modern Geography for the Use of Schools, by Robert Anderson. 



DEGREE IN ILLUSTRATION 311 

"At this rate it would have taken from 1000 years before the 
creation of man till now, in order to reach even Saturn." 

This old illustration is not introduced for its own sake, 
but because of the effect it produced on certain students 
to whom it was presented. Their attitude was at once 
that of the superior person. They did not quote 
Moliere, but they led me clearly to understand that we 
had now changed all that, and that thanks to the 
Mauretania and her rivals we could now cut down these 
distances by exactly one-half. So difficult is it to keep 
the relative and the absolute in their proper places. 
To be sure, the young men immediately saw their error, 
and one of them justified himself to some extent by 
saying that, after all, America is really nearer to Europe 
than it was last century; and to gainsay him was not 
the part of one who teaches that the true meaning of an 
idea is the power to behave intelligently in relation to 
the content of the outer world involved in that idea. 

Two summers ago at Niagara I read one of those folder 
advertisements of which such effective use is made in the 
States. Its purpose was to enhance the wonders of 
the falls. The length, breadth, thickness, and weight of 
the body of water were given, and after the mind had 
been sufficiently harrowed, the climax was reached by a 
statement of the length of time that it took for a cubic 
mile of water to fall over. I do not remember the exact 
figures of the folder, but have a vivid recollection of the 
sense of anticlimax involved. On calculating out the 
whole matter, I find the effect even more flattening than 
my memory led me to expect. Taking the figures 
supplied in the ninth edition of the Encyclopcedia 
Britannica (these are old enough not to allow for any 
diversion of water for the power stations, and thus 



312 EXPOSITION AND ILLUSTRATION IN TEACHING 

give the falls a fair chance to show up well), I find that 
18,000,000 cubic feet of water fall over every minute. 
This is sufficiently impressive, but when worked out 
on a volumetric basis the best we can say for the falls 
is that they toss over an entire cubic mile in five days 
sixteen hours/ The impressiveness gained by using 
the magnificent unit of one cubic mile is not nearly 
sufiicient to counterbalance the enormous loss in actual 
digits. 

Few people are able to realise what a cubic mile 
means. In fact, the calculation we have just made has 
enabled us to understand better what is implied in the 
higher unit, and so far is of use. But the question we 
are at present considering is the illustrative value of 
the cubic mile unit, not the possibility of realising that 
unit. In point of fact, we have here reversed the parts 
played by the illustration and the illustrandum. The 

^ A little personal experience is perhaps in order here : at any 
rate, it is instructive. In a lecture before the College of Preceptors 
in London in May, 1909, I used this illustration, but I made a mis- 
calculation to the extent of misplacing a decimal point. Though my 
result was thus ten times less than it should have been, it seemed 
big enough to correspond to what I remembered from the folder, so 
my suspicions were not aroused. In the correct verbatim report in 
the Educational Times for June 1 appears the passage: "The best 
we can do is to say that in thirteen and a half hours a whole cubic mile 
of water tumbles over the cliffs." No one wrote to correct this serious 
blunder : but I am not now surprised that the usually vigilant arith- 
matician forgot his customary lust for accuracy. Not that the state- 
ment remained unchallenged. Without troubling to work out details, 
an acquaintance — an astronomer of all men — said there must be 
something wrong, as it certainly could not take so long as thirteen and 
a half hours for a cubic mile of water to tumble over the cliffs; he 
had seen the falls and he knew. It was because of his objection 
that I revised my calculation, and now I find it very hard to get any- 
body to believe my result — so universal is the inability to realise 
what a cubic mile actually means. 



DEGREE IN ILLUSTRATION 313 

effect of the present paragraph has been to illustrate the 
enormous bulk of a cubic mile by means of the Falls of 
Niagara. If it takes even these gigantic falls five 
days sixteen hours to hurl over one cubic mile of water, 
then we may have some idea of what this unit implies. 

To obtain a pictorial conception of a cubic mile is not 
only difficult, but is of doubtful utility. In climbing an 
Alp we may be fortunate enough to come across a preci- 
pice that is just about a mile deep, and has certain rela- 
tions with neighbouring landmarks that enable us to 
separate out approximately a cubic mile of air-filled 
space. The effect is almost always disappointing. 
The mile seems^much smaller than we had expected, for 
the obvious reason that under the conditions sketched 
the surroundings are on such a grand scale that the 
imaged mile is dwarfed by its environment. Some 
prefer to get their conception through the medium of 
water. By noting certain distances on shore, and by 
fixing certain marks at sea, they get a square mile 
marked out, and then proceed to overwork their imagi- 
nation in an attempt to figure out the cube of water of 
which the marked square mile is the upper face. The 
important point, however, is not to make a picture of a 
cubic mile, but to realise by practical applications what 
it actually means. 

Many illustrations aim at the pictorial when they 
should really seek to eliminate it. The pupil is told 
that there are approximately sixteen hundred million 
human beings at present living upon the earth. It is 
difficult to realise this vast number, so the illustrator 
sets about making a picture. He selects some particu- 
lar part of the world that will just hold all the inhabit- 
ants of the earth standing packed together. The best 



314 EXPOSITION AND ILLUSTRATION IN TEACHING 

situation is obviously an island, because the imagination 
will have the aid of the sea in limiting its operations. 
It is well that the island selected should have some 
hill from the top of which the whole island can be 
envisaged. The Isle of Wight in the south of England 
fulfils this condition almost perfectly. Standing on 
Ashey Down, the spectator can command the whole 
island with a very trifling exception. The illustrator 
now proceeds with his calculations. The island covers 
about 147 square miles, and each square mile contains 
27,878,400 square feet. Accordingly, the island in- 
cludes 4,098,124,800 square feet. This, divided by 
1,600,000,000, gives 2.56 square feet per human being, 
or a square of about 19 in. side — just standing-room. 
Having now gathered the whole human race on the 
Isle of Wight, what better off are we? So far from 
being helped, the imagination is harassed. It has to 
work overtime, there are so many things for it to do 
with this huge crowd. The scene calls up too many 
irrelevant elements; we falter in our attempts to realise 
the different sizes, colours, and odours of those people 
swept in from all ends of the earth. How are they to be 
fed ? Are we to picture them as arranged by nations or 
indiscriminately ? How could they stand on some of the 
steep places in the island ? I have seen many a class 
reduced to desperation by the surging questions raised 
by this preposterous picture. As a preliminary to a 
word-picture of the Day of Judgment, the scheme 
may have its advantages, but for giving an idea of the 
population of the world it is not very successful. In 
actual practice it conveys the general impression that 
there are not so many people in the world after all. 
England itself is not very big, but the Isle of Wight is 



DEGREE IN ILLUSTRATION 315 

such a little place. If the purpose is to show how 
much room there is still in the world, the illustration 
is effective enough, though it could hardly be used as a 
fair argument. 

The best appeal is always to the highest unit available 
in the experience of the persons concerned. Taking 
the biggest city with which the pupil has personal ac- 
quaintance, this could be compared quantitatively 
with the number of people in the pupiFs native country, 
and then with the world population. The United 
States has a population that is rapidly approaching the 
good-natured number 100,000,000, so the American 
boy will soon have the advantage of a ready-made stand- 
ard that renders comparison very easy. It does not 
follow that the American boy realises what the popula- 
tion of his republic means. Yet all that is necessary for 
intelligent comparison is present. 

We need a standard unit for our illustrative work, but 
it is not always necessary to reduce our quantitative 
illustrations to this standard unit. It is enough if we 
have a unit to which we can reduce them all, if that be 
necessary. We ought to have a clear idea of what one 
square foot means, an acre, and if possible, a square 
mile. In certain towns the municipal authorities are 
good enough to lay out somewhere in their parks a 
square acre, so that the children of the town may grow 
up accustomed to this as a standard. The Bank of 
England, in London, we are told, covers exactly one 
acre of ground, but this is not nearly so useful a standard 
as the square acre. The bigger the quantities we are 
to deal with, naturally the bigger the standard unit. 
With certain astronomical measurements the unit is 
the radius of the earth, with others the diameter of the 



316 EXPOSITION AND ILLUSTRATION IN TEACHING 

moon's orbit, with still others the major axis of the 
earth's orbit. Whatever the standard, it must be a 
definite one. The ordinary householder is so perplexed 
at the unintelligible order to put one fluid ounce of 
pepsin in a quart of milk that he welcomes the prac- 
ticable if inexact equivalent of two tablespoonfuls. 
But in deliberate illustration, some sort of standard 
should be insisted on, and should not be changed in the 
process of Exposition or Illustration, In working with 
money values, for example, we may have occasion to 
deal in several different coinages; but it is always better 
to keep to one as the standard during any one series 
of calculations. Dollars are easily valued in pounds 
sterling as we go along, without any great inaccuracy; 
but there is a great deal of time wasted and a certain 
danger of confusion incurred by continually passing 
from the one to the other. Some tourists on the Conti- 
nent of Europe make life a burden to their friends by 
dividing by eight and multiplying by &ye at every kilo- 
metre stone. In a kilometre country we should accept 
the 1000-metre standard. After tramping for a day or 
two, '^32 kilometres" is as clear a conception as is 
^'20 miles" at home. Of course where actual contrast 
between the two standards is the immediate purpose, 
there must be continual interpretation of one in terms 
of the other. But in most cases there is no need for a 
double standard, and usually one or other is marked 
out as naturally more suited for the particular bit of 
Exposition in hand — dollars in the United States, kilo- 
metres in France-; inches in a popular description, centi- 
metres in a scientific analysis. 



CHAPTER XIII 

Material Illustrations 

When we try to classify illustrations, we encounter 
certain difficulties. The first broad distinction that 
suggests itself among the various kinds of illustration is 
that between the real and the verbal. There seems a 
very important difference between mere words on the 
one hand, and such aids as objects, models, and draw- 
ings on the other. But while the distinction has a cer- 
tain convenience, it must be remembered that both 
real and verbal illustrations make their appeal primarily 
to the same set of forces : the only way they can get at 
the mind is by rousing ideas. But an idea may be 
called up by a word as well as by an actual object, so 
that the two kinds of illustrations are practically one on 
the psychological side. There is the more need to insist 
upon this because of a very general impression among 
teachers and others that there is an inherent superi- 
ority in things as compared with mere words as a means 
of illustration. But here, as elsewhere, ^^each thing in 
its place is best.'^ It has to be remembered that verbal 
illustration has certain advantages. It is much freer 
than illustration by means of actual objects: it gives 
much more scope for the action of the mind appealed to, 
since in any case only the content already acquired can 
be used. The clergyman who produces an actual lily 
in the pulpit to illustrate his sermon on purity thinks he 

317 



318 EXPOSITION AND ILLUSTRATION IN TEACHING 

has used a stronger illustration than if he had merely- 
referred to the flower. All that has happened is that 
he has aroused a certain amount of extrinsic interest 
that he must be exceedingly careful to turn into in- 
trinsic interest in his subject before he can hope to profit 
by it as an illustration. The children can take out of the 
lily only what they were able to put into it before it 
appeared in the pulpit. Anything the clergyman can 
tell them about the lily as a plant will no doubt increase 
the knowledge of some of the children. But this is the 
result of information rather than of illustration. If the 
clergyman were dealing with botany, the relation be- 
tween the lily and his subject would be different. 

We must clearly distinguish at this stage between an 
ob j ect as a sub j ect of study and as an illustration. When 
we are giving instruction on some actual object, say in 
chemistry, botany, or geology, nothing can make up 
for the absence of that object. People are now agreed 
that in practical subjects we must depend upon practi- 
cal work.^ Nothing can make up for the lack of labora- 
tory and field work. Text-book teaching of practical 
subjects is now universally condemned. But this 

* This is the general view ; but there are dissentients. Mr. H. W. Eve, 
an emeritus headmaster and distinguished physicist, told me the other 
day that there was no need for the pupil to do the experiments : all 
that was necessary was that he should understand a description of 
them. Sir William Ramsay says, "Far too much stress is laid, now- 
adays, on what is called 'practical work.' It is possible to have 
quite an intelligent idea of chemistry without ever having handled 
a test-tube or touched a balance. Lectures on chemistry may be well 
illustrated experimentally, and the necessary theories demonstrated 
by the lecturer. ... To spend several hours a day in practical work 
is, if not a waste, often, at least, a work of supererogation." Quoted 
by Dr. F. H. Hay ward in his stimulating book, The Meaning of Edu- 
cation (p. 15). 



MATERIAL ILLUSTRATIONS 319 

does not at all imply that a test-tube is inherently a 
better illustration than a metaphor. In the mind of 
the teacher there is too often a sort of descending scale 
of merit in which possible illustrations are arranged 
somewhat in this way : — 

(1) The real object, for which anything else is a 
more or less inefficient substitute. 

(2) A model of the real object. 

(3) A picture of the object. 

(4) A diagram dealing with some of the aspects of the 
object. 

(5) A mere verbal description of the object. 

Assuming that the teacher's purpose is to give infor- 
mation on the object, the above order of merit may to a 
large extent be justified. But it should not be forgot- 
ten that under these circumstances we are dealing with 
information and not with illustration. Too frequently 
the above general order of merit is carried over to the 
purely illustrative field, and we have an unwarrantable 
glorification of ^^ objects.'' 

Even with regard to what is properly called instruc- 
tion on a given real object, there are certain respects 
in which a model or a picture may be actually of more 
service than the thing itself. It has to be admitted 
that it is not always possible to present to the pupils 
the real thing. In all cases this is to be regretted. It is 
a pity that such things as Magna Charta, an elephant, a 
locomotive, the Port of Bordeaux, cannot be brought 
to school. The teacher has reluctantly to do without 
them, unless he is able to take his class where these things 
may be seen. With this desire for the real we must all 
sympathise. But it is worth while noting that there 
are certain stages in instruction when a model is not 



320 EXPOSITION AND ILLUSTRATION IN TEACHING 

only as good as, but better than, the object it represents. 
In other words, the model actually illustrates the real 
object. Sometimes the object is too large to be taken 
in at one sweep of the eye, and is therefore difficult to 
deal with. A large and complicated machine — take, for 
example, a certain paper-making machine that as a 
matter of fact covers an area of over two thousand 
square feet — may be far better understood from a 
small working model than from the machine itself. So 
with extremely small objects it is sometimes very desir- 
able to have a magnified model for illustrative purposes. 
It is obvious that, in using a model, abstraction must 
be made: the model must lose some of the qualities 
that belong to the real object. Sometimes the ab- 
straction is confined to size. The model resembles the 
original in every respect except that it is either larger 
or smaller. A model locomotive may be an exact re- 
production of one in actual operation on a railway. 
On the other hand, it may be slightly changed in certain 
details and yet convey the general impression of being 
the same as the real locomotive; and the internal va- 
riations may increase in amount, each new variation 
marking a higher degree of abstraction. For example, 
the model may have exactly the same machinery as 
the original, but the heat may be produced by burn- 
ing methylated spirits instead of coal; and there are 
obviously all the degrees of increasing abstraction 
till we reach the child's toy that preserves the outward 
show, but is worked within by a spring. A model at any 
of these grades of abstractness may have its use as 
illustration, everything depending on the nature of the 
illustrandum. For the student of engineering the 
model must be so accurate that he can make from it 



MATERIAL ILLUSTRATIONS 321 

measurements to scale. On the other hand, in teach- 
ing mechanics, a clockwork locomotive is quite good 
enough to illustrate certain problems of gradients. 

In the case of students studying ''in the field" the 
structure of a district of country, say the Great Lake 
area in the St. Lawrence basin, it is found to be very 
difficult for them to have a grasp of the whole situation. 
They can see now this part and now that, but they cannot 
from any one point envisage the whole. Accordingly, 
they are set to make a relief map of the district in clay 
or plasticine. This is really a model of a high degree of 
abstractness. To begin with, it must be so accurately 
worked that calculations may be based on it, allowance 
being made for the difference between the horizontal 
and the vertical scale. But the only real points of 
resemblance between the model and the district are in 
the proportions of the dimensions. The material used 
is of no consequence. Of course in a more elaborate 
scheme the different strata might be represented by 
layers of different coloured clay contorted so as to rep- 
resent the actual formations. Sometimes, indeed, very 
elaborate models of this kind are made in glass, so that 
the pupil may, from the side of the case, observe the 
various dips of the strata, and note the faults. But 
even here the material is not significant of the illus- 
trandum. 

In the case of a model to represent that bridge over 
the Hhine that has given so much trouble to every 
teacher who has piloted a class through Caesar^s Com- 
mentaries ^^ it would appear to be possible to make the 
model correspond to the original in all the respects with 
which we are acquainted. While such a model, made 
1 Book IV, Chap. XVII, 



322 EXPOSITION AND ILLUSTRATION IN TEACHING 

exactly to fit the conditions laid down in Caesar's text, 
may be an excellent illustration of that text, it does not 
follow that it is a good illustration for the use of a party 
of men proposing to make a bridge over the Rhine, 
and that not because engineering has advanced since 
Caesar's time, but because the whole problem of the 
strength of materials has to be recast according to the 
actual dimensions of the real bridge. Stresses and 
strains do not have the same effect upon the same mate- 
rial under different conditions of dimension. This is 
why practical men in general, and engineers in particu- 
lar, use models for certain parts of their work, but pre- 
fer to test their results on the true scale before they are 
wiUing to apply them. 

In the case of class work our principle should be the 
same as the engineer finds useful in his actual operations : 
begin with the real object, and end with the real object, 
but between the two use the model as freely as you like. 
In school we very commonly use models that involve 
a high degree of abstraction. In the teaching of botany 
we may have a greatly enlarged model of the primrose 
made of papier mdche. The form may be a perfect 
reproduction of that of the real flower; the colour a some- 
what less accurate reproduction. But there the resem- 
blance stops. Abstraction is made of size, flexibility, 
moisture, texture, scent. The sole value of the model is 
that its size enables the teacher to give a demonstration 
to the whole class. To facihtate this the model is made 
up of distinct parts which can be separated from each 
other so that the teacher can make a formal dissection 
of the model, which dissection may be afterwards imi- 
tated by the members of the class while dealing with 
the real specimens with which they are then provided. 



MATERIAL ILLUSTRATIONS 323 

For, wherever possible, the teacher should follow the 
example of the engineer, and end all his model work 
by a reference to the actual object. The pupils should 
begin with an examination of a real primrose actually 
growing in the garden or in a pot. Then comes the 
demonstration on the magnified model, and finally 
the examination by each pupil of the cut specimen 
supplied. 

The same sort of models are used in the teaching 
of biology. The cockchafer is selected as the typical 
insect, and there is a highly complex dissectible model 
constructed for class demonstrations. But a still higher 
degree of abstraction is reached in a series of hollow 
models of some forty animals produced by a well-known 
maker of school apparatus. One can understand the 
use of models in illustrating the outward appearance 
of such creatures as the elephant, the camel, and the 
bear; but when it comes to the horse, the cow, and the 
dog it may be naturally asked wherein consists the use- 
fulness of a set of models of creatures that may be con- 
veniently seen in real life. One obvious answer is that 
the models indicate the relative sizes of the different 
animals; for in the series referred to the creatures are 
all made to a common scale. In the next place, the 
models are available in school, and enable the pupils to 
make certain observations that may be tested by a 
later examination of the actual animals as found in the 
open air. The objection that the models are mere 
shells of animals is hardly of much consequence. The 
child sees as much of the inside of the model cow as he 
sees of the inside of the cow in the field. Further, 
such models rouse an interest in familiar animals that 
the animals themselves cannot command. Just as the 



324 EXPOSITION AND ILLUSTRATION IN TEACHING 

COWS in a landscape in a drawing-room attract much 
more attention than they ever did in the meadow, so 
the models in school interest the children more than do 
the real animals — always taking it for granted that 
we are dealing with animals that have exhausted the 
charms of novelty. A papier mdche camel has little 
chance of surpassing the attractions of the live one. 
But in the case of the horse it is different. Most of 
us will look with interest at a model of something that 
we pay no attention to when we meet it in real life. 
Advertisers have not been slow to profit by this interest 
in models, as is seen by the many tiny samples sent out, 
in which the characteristic bottle or packet that con- 
tains the commodity is exactly reproduced, but on a 
very small scale. The same interest is appealed to 
when the advertiser sends out a cart bearing a mam- 
moth representation of the bottle or packet. 
i'lt goes without saying that the special value of the 
model lies in the fact that it gives us all three dimensions. 
It is therefore assumed that it is necessarily a better 
form of illustration than anything in the way of a draw- 
ing, which, after all, can never get beyond tv/o dimen- 
sions, with a suggestion of the third. The model may 
be viewed from many different standpoints, and against 
different backgrounds. It is sometimes said that a 
model of the reconstructed Parthenon at Athens con- 
veys a much more accurate conception of what it was 
once like than can any mere plan and elevation sketches. 
But for certain purposes a picture is a better illustration 
than a model. For example, a picture of the Parthe- 
non painted by a sympathetic artist, with the model 
to keep him right in detail, and his own trained imagi- 
nation to interpret in terms of colour the old surround- 



MATERIAL ILLUSTRATIONS 325 

ings, will probably convey a better impression of what 
was the real state of things in old Athens than does 
the mere dead model. This is perhaps a characteristic 
of the model, that it confines itself to the bare primary 
details. The artist's lay figure does all that is expected 
of it when it keeps him straight with regard to the 
three dimensions. Within these limits it does its work 
admirably, but it carries with it no suggestion of reality. 
There is always something unreal in a complicated 
model that is not necessarily present in a picture. 
Take, for example, those elaborate models of various 
cities and ports that have been exhibited at certain of the 
great exhibitions in different parts of the world. (A 
permanent collection of this kind is to be seen in the 
upper regions of the Louvre in Paris.) The observer 
has thrust upon him an inevitable feeling of triviality. 
The models have all the appearance of toys. They 
are excellent to work from. They give us a general 
view of the city and its approaches such as we could not 
get from any available point of view in the district. 
We can in a few minutes, by means of compasses and 
scales, get any desired measurements. But we cannot 
get rid of the feeling of unreality and childishness. 
So in dealing with the accurate models of great build- 
ings of which the Germans are so fond. These models 
are excellent in demonstrating shapes and measure- 
ments, but they are useless in reproducing the aesthetic 
effect of the actual buildings. We can extract no en- 
thusiasm from a model of St. Peter's at Rome. The 
abstraction of size has destroyed its power to impress us. 
Models of the Gothic Cathedrals have a stronger aes- 
thetic effect upon us than have models of the severer 
buildings of the classical times. When the old temples 



326 EXPOSITION AND ILLUSTRATION IN TEACHING 

have lost the grandeur that their spaciousness gave them, 
they have nothing left. The Gothic Cathedrals, too, lose 
their grandeur, but in its place there comes a certain 
prettiness. Awe is a sentiment that cannot be repre- 
sented on a reduced scale. Models can reproduce pro- 
portions, but not sentiments. They have all the defects 
of the diagram as well as its merits. They are indeed 
nothing more than three-dimensioned diagrams. 

It is because we live in a three-dimensioned world 
that the model deserves a place among our illustrative 
apparatus. Our daily experience makes it impossible 
for us to overlook the third dimension ; but overf amiliar- 
ity with two-dimensioned illustrations is very apt to lead 
to an unintelligent way of regarding certain matters. 
The globe, for example, is necessary to counteract the 
impression produced by the ^^ World in Hemispheres ^' 
as it is presented to us at the beginning of our atlases. 
It is true that the globe in its turn is subject to abuse. 
In his usual aggravating way Eousseau makes us uncom- 
fortable by calling it nothing but a plaster ball. But 
the teacher does not want it to be anything else. So 
long as he uses it as an illustration he is proclaiming that 
it stands for something that it is not. Its merit is in 
its shape, not in its material. This shape prevents the 
illustrator from taking certain liberties that he allows 
himself when he has got rid of the third dimension. 
He wants, for example, to show that the British Isles oc- 
cupy the enviable position of being in the very centre 
of the land hemisphere. Accordingly, he does violence 
to all the known systems of map projection and com- 
bines the two hemispheres into a heart-shaped whole. 
The British Isles appear in their true projection on the 
middle hne that marks the junction of the two halves of 



MATERIAL ILLUSTRATIONS 327 

the heart, while all the rest of the world wriggles about 
in greater or less degrees of distortion. The proper 
way to illustrate the fact of the central position of the 
British Isles is to take up a globe and turn it so that the 
pupil is looking at it in such a way that he sees the great- 
est total amount of land that it is possible for him to 
include in one view. Once the model-world is placed in 
this position, the pupil is invited to look for the British 
Isles. As a matter of fact, he will find them not far 
from the centre of the part of the world at that moment 
visible on the globe. 

It is in connection with the seasons and the rotation of 
the earth that the use of a tangible ball is of importance 
as an illustration. No doubt in teaching such matters 
as longitude and latitude it is necessary to have a prop- 
erly constructed globe, with all the conventional signs 
properly filled in. The practical teacher is very often 
tempted to regard this orthodox globe, with its axis 
fixed at the proper angle of 23J°, as itself the illus- 
trandum. He talks about * teaching the globes,'' 
whereas what he wants to say is that he teaches certain 
relations by means of the globe. When the earth's 
relation to the sun and to the other planets is to be 
illustrated, it is better to have a less formal ball to deal 
with. In practice it is found that a ball of worsted 
with a knitting needle thrust through the middle to 
represent the axis is about as useful a form of globe as 
can be found. Each pupil should be supphed with 
such a ball, and should be called upon to manipulate it 
as the teacher describes certain of the phenomena of 
the earth's rotation and revolution. At the testing 
stage it is well that only one pupil at a time should 
manipulate a ball, as, if the class works collectively, 



328 EXPOSITION AND ILLUSTRATION IN TEACHING 

there will be little else than imitation in the case of a 
great many of the boys. 

A very interesting comparison of the relative values 
of the two-dimensioned and the three-dimensioned 
illustration may be had from comparing the results of 
teaching from a diagram and teaching from the use of 
the ball. The familiar diagram of the sun at one of the 
foci of an ellipse with the earth in the four positions 
on the circumference corresponding to the four seasons 
may be fully understood by the class. That is, the 
pupils may be able to say honestly that they understand 
the diagram and are able to answer questions on it. Now 
arrange for an experiment. On a table on an open 
space on the floor place a candle or anything else that 
will represent the sun, and then call out one of the 
pupils and ask him to carry his ball of worsted round the 
supposed sun, in such a way as to represent the revolu- 
tion of the earth, and thus demonstrate the cause of 
the seasons. In a large percentage of cases in which 
this experiment has been made, the pupil moved round 
the sun, keeping the axis jealously fixed at what he 
believed to be 23J° from the vertical, but point- 
ing at the sun all the time. This occurs even when 
stress has been laid by the teacher on the fact that the 
earth's axis is always '^'parallel to itself.'' The fixed angle 
of 23J° satisfies the mind's requirement in this respect, 
and nothing short of the Confrontation implied in the 
permanent winter of the side remote from the sun in 
the actual experiment will rouse the pupil to the neces- 
sary dissatisfaction with his view as gathered from the 
plane diagram. 

An orrery supplies a striking example of ineffective- 
ness in illustration. The motions of the planets and 



MATERIAL ILLUSTRATIONS 329 

their satellites can be reproduced in a very accurate 
way, but the mental effect of the whole is discouraging. 
The distance effect is as much lacking here as in the 
case of models of huge buildings. Sir John Herschel 
speaks very strongly of the futility of giving an idea of 
the sizes and distances of the planets by this means, 
and sets forth a scheme of his own to convey the desired 
information : — 

"Choose any well-levelled field or bowling-green. On it place 
a globe two feet in diameter ; this will represent the sun ; Mercury 
will be represented by a grain of mustard seed, on the circumference 
of a circle 164 feet in diameter for its orbit ; Venus a pea, on a circle 
284 feet in diameter ; the Earth also a pea, on a circle of 430 feet ; 
Mars a rather large pin's head, on a circle of 654 feet ; Juno, Ceres, 
Vesta, and Pallas grains of sand in orbits of from 1000 to 1200 feet ; 
Jupiter a moderate-sized orange, in a circle nearly half a mile across ; 
Saturn a small orange, on a circle of four-fifths of a mile ; Uranus a 
full-sized cherry, or small plum, upon the circumference of a circle 
more than a mile and a half ; and Neptune a good-sized plum on a 
circle about two miles and a half in diameter. As to getting correct 
notions on this subject by drawing circles on paper, or, still worse, 
from those very childish toys called orreries, it is out of the ques- 
tion.^' ' 

This illustration fails in many directions. To begin 
with, there is a lack of a definite standard of size. 
What is the standard size of a pea, a cherry, a plum, an 
orange ? Who is to determine how big a large pin's 
head is ? Further, whatever the real size of a pea, the 
effect that the illustration produces on the mind of the 
ordinary reader is that Venus is larger than it really is 
in proportion to the earth. If it is said that all that is 
wanted is to convey a general impression, the answer 
is that the illustration invites comparisons, and suggests 

^ Outlines of Astronomy (1849), p. 323. 



330 EXPOSITION AND ILLUSTRATION IN TEACHING 

by its discrimination among the various qualifying 
adjectives that the comparisons are accurate. Again, 
the distances should be kept to the same standard: 
they ought all to be expressed in feet. These criticisms 
are not the outcome of arm-chair reflection. They 
express the complaints of many classes of students 
(ages ranging from eighteen to twenty-one) who have 
been offered instruction through this illustration. 

The truth is that what are called real illustrations, 
those that deal with actual objects, have the defects of 
their quality, and fail because of the very virtue on which 
real illustration prides itself — reality. Three-dimen- 
sioned illustrations sadly hamper the freedom of the 
pupil's imagination. If we are to picture certain grains 
of sand in a preposterous bowling-green two and a half 
miles wide, we find that, so far from being helped by our 
illustration, we are really hindered in our efforts to 
figure out the sizes and distances of the planets. Her- 
schePs illustration certainly aids us in respect of the 
concept of distance, and gets rid of the toy effect 
of the orrery; but in so far as it substitutes peas and 
cherries for the spheres of the orrery, it introduces limit- 
ing elements. After all, a diagram leaves the mind 
freer than do these concrete comparisons. 

Sir John Herschel's illustration has been largely used 
by teachers, and it is interesting to note the changes 
they have made. It is generally used in schools in tabu- 
lar form rather than as a description. Venus is rep- 
resented by ^'a pea," but the earth by '^ a larger pea" — 
so strong is the teacher's love of accuracy and the pupils' 
of fair play. The only other important change is that 
many teachers prefer to cut down the distances by one- 
half, taking the radius in preference to the diameter. 



MATERIAL ILLUSTRATIONS 331 

Another debatable use of the solid as illustration is 
to be found in the glyptic formulae of Hofmann. Not 
content with the elaborate patterns of the graphic 
formulae that were used to represent such complicated 
chemical combinations as Dicobaltic tetrammon-hexa- 
ammonic hexachloride (called purpureo-cobalt chloride, 
for short), Hofmann launched out into the third dimen- 
sion, and invented a system of spheres of about the size 
of billiard balls ^ of various colours, each having one or 
more little tubes projecting from its surface, accord- 
ing as it was intended to represent a monad, a dyad, 
or an atom of some higher valency. By means of con- 
necting rods of various curvature, Hofmann was able to 
build up symmetrical combinations to indicate how the 
elements united with each other and formed more or 
less permanent wholes. It is doubtful whether any- 
thing was gained by all this elaboration, for the 
models did not even pretend to reproduce a state of 
affairs that actually existed. If Sir John Herschel 
fails in making us realise the solar system, it is because 
we cannot properly represent what actually exists. 
In the case of the chemical formulae, the teacher has to 
warn his pupils against imagining that what he sees 
in the model represents what actually takes place in 
chemical process. Dr. Edward Frankland, of the 
Royal College of Chemistry, London, himself an excel- 
lent teacher, made extensive use of both glyptic and 
graphic formulae. He tells us in the Preface to his 
well-known compendium : ^ — 

^ Later, the tetrahedral form was introduced to enable the teacher 
to give demonstrations of combining molecules by means of common 
elements. 

2 Lecture Notes for Chemical Students, 1866, 



332 EXPOSITION AND ILLUSTRATION IN TEACHING 

''I am aware that graphic and glyptic formulae may be objected 
to on the ground that students, even when specially warned against 
such an interpretation, will be liable to regard them as representa- 
tions of the actual physical position of the atoms of compounds. 
In practice I have not found this evil to arise ; and even if it did 
occasionally occur, I should deprecate it less ^ than ignorance of all 
notions of atomic constitution." 

But surely the concluding sentence is somewhat 
strong. Are we shut up to the alternative of glyptic 
formulae or ^ ignorance of air notions of atomic consti- 
tution'^ ? The fact is that there are types of mind that 
find the glyptic formulae repellent, and others that revel 
in them with such delight as to lead to danger of con- 
founding the illustration with the illustrandum. The 
other day a student of the second type brought forward 
a scheme for making ''a model of the mind" on glyptic 
principles. Each idea was to be represented by a ball, 
and the apperception masses were to be built up sepa- 
rately, and then combined with each other by uniting 
the different masses by means of common elements. 
Reflection for a few minutes shows how unworkable the 
scheme is, and yet it has great possibilities in the way 
of illustration. One of its main advantages would be 
that it would convince the students that an atomic 
theory of ideas is only an illustration of a system that 
cannot be fully explained on this basis. 

When material illustrations are used in connection 
with solid geometry, they have to fulfil the very function 
that Dr. Frankland warned his students against. They 
must be ''representations of the actual physical posi- 
tion '^ of the elements of the illustrandum. There can 

1 Yet it was with regard to one of the plates of graphic formulae 
in Dr. Frankland's book that the Oxford don remarked, " Ah, I sup- 
pose that is how the gases look under the microscope." 



MATERIAL ILLUSTRATIONS 333 

be no question of the value of cardboard models in 
illustrating the exasperating little diagrams that adorn 
the eleventh book of Euclid, even though the severe 
mathematician looks askance at any attempt to rep- 
resent the realities of which he makes abstraction. 
In projection, sections, development, and penetration 
the use of standard models is of the greatest value. 
Often all that is wanted is a glance at the actual model. 
It is different with some of the elaborate apparatus de- 
vised to make dull students understand the projection 
of points and lines on the two coordinate planes. After 
taking many classes through a course in descriptive 
geometry, and using with them all manner of appara- 
tus, I am convinced that, in teaching the elements of the 
subject, all the elaborate arrangements of beads and 
threads and pins are worse than useless. If the candi- 
date cannot understand the dots and lines above and 
below the line of intersection in a given diagram, he is 
not at all likely to understand the aggravating complica- 
tions introduced by way of illustration. This is one of 
the cases in which the illustrandum is clearer than the 
illustration. An arrangement in cardboard or wood by 
which the two coordinate planes can be represented as 
cutting each other, and thus showing the four dihedral 
angles and the line of intersection (almost universally 
named XF) is a simple piece of apparatus that should 
always be available. It is usually made so that the two 
coordinate planes may be made to rotate on XF so as 
to (practically) coincide, and thus illustrate the relation 
of the various dihedral angles to the plane of the paper 
on which the pupil's drawing is to be made. Such a bit 
of apparatus is extremely simple, and leaves the pupil's 
imagination quite free with regard to individual prob- 



334 EXPOSITION AND ILLUSTRATION IN TEACHING 

lems, while rigidly restricting it as to the conditions of 
all problems. 

Generally speaking, there is a tendency in all material 
illustrations to become too elaborate, and the teacher is 
apt to think that their value is in proportion to the 
amount of time he spends in their preparation. In 
actual teaching their value is often in inverse ratio. 
It is different in the case in which the pupils themselves 
take a part in preparing the apparatus. When this 
occurs, they acquire that familiarity with the subject 
that in the other case is confined to the teacher. 

The ideal use of teaching-models is to have them 
made by the pupils, not merely as teaching-illustra- 
tions but as a substantive part of their intellectual work. 
It is not a case of making things, but of thinking thoughts 
and expressing them in a material form. My colleague, 
Dr. T. Percy Nunn, has contrived to get several classes 
of quite young pupils to make drawings and models 
embodying their own observations of the sun and the 
moon, and has obtained astonishing results in the way 
of clear thinking on matters that greatly puzzle most 
adults. Boys of twelve, starting from the daily measure- 
ment of the sun's shadow at noon, have themselves 
worked out all the calculations necessary to develop the 
curve of the sun's apparent path through the heavens, 
and ended by making a cardboard model of this path 
in such a way as to make clear the relation between 
the apparent path of the sun and the real path of the 
earth. These boys talk on such matters now with an 
ease that disconcerts the ordinary educated man, who 
has always to pause and reflect before he ventures to 
make any statement that correlates the real with the 
apparent in the movements of the heavenly bodies. 



MATERIAL ILLUSTRATIONS 335 

Dr. Nunn himself writes : ''I always regard my models 
as being devices to aid the boy in ^colligating' his own 
observations. They differ from the usual models in 
not aiming at dispensing with first-hand observations. 
That is, I think, why they are effective. The boy 
thinks of the facts by the aid of the symbols.'^ 



CHAPTER XIV 

The Picture as Illustration 

From one point of view a picture is necessarily more 
abstract than a model. One aspect of reality is seized 
upon and elaborated. Even in the case of the mere re- 
production of reality in a photograph there is abstrac- 
tion. We are limited to one point of view and to the 
corresponding background. The model may be viewed 
from many standpoints, and from each standpoint there 
is a different background. All the laws of linear per- 
spective enrich the possibilities of models as illustrations. 
When we consider aerial perspective and the laws of 
colour, we find still further need for abstraction forced 
upon the picture as a means of illustration. The 
painter must select the particular set of colours that mark 
the moment chosen for the painting. The fact that the 
colours of an object or a scene change from hour to hour, 
almost from moment to moment, has always been known, 
but has of late years been more clearly recognised. 
The school of Impressionist painters have done valu- 
able work in bringing home to us this important fact. 
They claim that it is the artist's business to paint light 
as represented by colour. They ought to be called 
Chromatists rather than Impressionists. One cannot 
look at Claude Monet's series of hay-ricks or cathedrals 
without realising that one picture can represent only one 
out of many aspects of the same object in respect of 

336 



THE PICTURE AS ILLUSTRATION 337 

colour, just as it can represent only one aspect with re- 
gard to linear perspective. This painter's methods in 
his careful studies of light and colour have been thus 
described : — 

"He is said to take with him in a carriage at sunrise some 
twenty canvases which he changes from hour to hour, taking them 
up again the next day. He notes, for example, from nine to ten 
o'clock the most subtle effects of sunlight upon a hay-rick; at ten 
o'clock he passes on to another canvas and recommences the study 
until eleven o'clock. Thus he follows step by step the modifica- 
tions of the atmosphere until nightfall, and finishes simultaneously 
the whole series. He has painted a hay-stack in a field twenty times 
over, and the twenty hay-stacks are all different. He exhibits 
them together, and one can follow, led by the magic of his brush, 
the history of light playing upon one and the same object." ^ 

When we examine these early morning hay-ricks, late 
morning hay-ricks, noontide hay-ricks, afternoon hay- 
ricks, and evening hay-ricks, we find that each has its 
individuality, and yet there is only one ^'real hay-rick.'^ 
If there be this great range in the case of such an emi- 
nently good sitter as a hay-rick, what must be said of 
the portrait painter's work ? What help can we expect 
from a portrait in forming an idea of even what a man's 
outward appearance is like, to say nothing of what his 
character is? Some historical portraits are done in 
triplicate, the group including a front view and the 
two profiles. This gives us a certain amount of help, 
but for a complete illustration of the appearance of an 
historical character we would require a gallery of por- 
traits. Were it not that Velasquez was a court painter, 
we might look to his many pictures of Philip IV as at 

^ Camille Mauclair : The French Impressionists, English translation, 
p. 130. 

z 



338 EXPOSITION AND ILLUSTRATION IN TEACHING 

least approximate material for forming an idea of how 
that monarch really looked. 

In view of all this limitation in the case of persons 
who really existed, what are we to say when we come 
to deal with matters in which there is no longer any 
standard in existence ? If we are so doubtful about the 
mere face of an important character in an historical 
scene, we can realise to some extent how helpless we are 
in the hands of the historical painter. There are indeed 
as many Fields of the Cloth of Gold as there are painters 
who have ventured to reproduce the scene. Naturally 
this raises the question of the value of pictures in text- 
books of history. Some teachers object to any picture 
that does not confine itself to the mere details of dress, 
architecture, and general archaeological matters of which 
we have certain knowledge. From this point of view 
historical illustration is a sort of antiquated fashion- 
plate. The ideal illustrations would have to be culled 
from the learned German tomes that contain reproduc- 
tions of the fluctuating fashions throughout the cen- 
turies. 

Such teachers maintain that all pictures describing 
an actual incident must of necessity be wrong. The 
one thing that may safely be asserted about the incident 
is that, however it happened, it did not happen in just 
the way the painter has represented. Mathematical 
laws are invoked to prove the infinitely remote chance 
of all the. combinations coming right in a given repre- 
sentation of the incident. 

If you care to go to the Ashmolean Museum at Ox- 
ford, you will find under a glass case certain pieces of 
old iron that are labelled as being the identical lantern 
used by Guy Fawkes on a certain fateful fifth of Novem- 



THE PICTURE AS ILLUSTRATION 339 

ber. It does not appear that there is any question about 
the genuineness of the debris, and visitors are sometimes 
able to get up quite a pleasant degree of excitement at 
the sight of the scrap-iron. The fashion-plate teachers 
regard the remains with favour, and would willingly 
provide all English schools with at least a photograph of 
them in the unavoidable absence of the inspiring origi- 
nals. To these teachers a spirited picture of the arrest 
of the traitor is regarded as dangerously misleading, 
because it cannot possibly be 'Hrue." 

''Do these little people," we may ask, with a distinguished 
American novehst, "know that Scott's archaeology was about one 
thousand years 'out' in Ivanhoe, and that to make a parallel we 
must conceive of a writer describing Richelieu, say, in small 
clothes and a top hat ? But is it not Richelieu we want, and Ivan- 
hoe, not their clothes, their armour ? " ^ 

All the same, while a protest is necessary against the 
excessive attention given to archaeological details, there 
is nothing to be gained by deliberately neglecting them. 
// Scott is one thousand years wrong in his archaeology, 
it is something to be condoned, not admired. Veronese's 
picture of the ^'Marriage at Cana'' is perhaps none the 
less a masterpiece, though he has put the people into the 
clothes of his contemporaries; but the work is not im- 
proved by the anachronism. As teachers we must be as 
accurate as we can without becoming pedantic. 

The points to be determined in connection with a 
picture of an historical scene as illustration are mainly 
two: the one negative, the other positive. First, the 
picture must not contain anything that contradicts 
historical evidence; it must be consistent with all that 
we know of the period. Secondly, it ought to throw 

* Frank Norris : The Responsibilities of the Novelist, 1903, p. 17. 



340 EXPOSITION AND ILLUSTRATION IN TEACHING 

some light on the scene depicted; it ought to embody 
an idea. 

It is obvious that a picture may fulfil both these 
conditions, and at the same time do a great deal to 
teach the details of the dress, architecture, and mode 
of living of the time. The danger is that these details 
may become too prominent, and the picture acquire 
that purposeless air that marks the fashion-plate. A 
novel with a purpose is usually a poor novel, because it 
was not the writer's main purpose to make a good novel. 
So the fashion-plate picture fails because its purpose 
is to be a good fashion-plate, and not to be a good 
picture. 

It has to be remembered that every picture, historical 
or other, however well executed, limits the mind of the 
spectator in dealing with the scene depicted. Once a 
set of elements have been combined in a definite way, the 
mind finds it difficult to break up the connection and 
recombine them. Young clergymen of great ability 
and originality have complained that they had to give 
up reading the published sermons of the great English 
preacher, Robertson, of Brighton, for the reason that 
once they had read one of these sermons, the text re- 
mained ever after a forbidden one for them, since it was 
impossible to preach upon it without seeming to 
have plagiarised. The treatment of the subject in the 
printed sermon seemed to them so thorough and 
altogether so satisfactory, that there appeared to be no 
other way in which it could be properly dealt with. 

The same difficulty is experienced by anyone who 
wishes to make a new illustration of some principle that 
is stated and particularly well illustrated in a text-book. 
The combination of elements is so well made in the 



THE PICTURE AS ILLUSTRATION 341 

original illustration that the reader finds his way blocked. 
He may break up the illustration into its constituent 
ideas, but these show a strong tendency to recombine on 
their old lines. While this is true of all sorts of combi- 
nations, it is particularly true of those that have been 
formed in spatial relations. A description of a certain 
incident may be given, and the hearer may make a 
more or less vivid mental picture of the occurrence ; 
still, as a rule, this picture can be easily replaced by 
another. But if the scene has been expressed in terms 
of space and colour in an external picture, it is very diffi- 
cult indeed to make a mental reconstruction. The less 
exact the verbal description the more dangerous is the 
external picture as a determining force, for the more 
is left to the draughtsman. Poetry, for example, is sel- 
dom well illustrated. For this there are two reasons. 
First, it requires a poet to illustrate a poet. So far 
as the readers of a poet are able to appreciate his 
writings, so far are they also poets, though they play a 
more passive part than that of the poet who writes. 
Apart from power of execution, the minimum demand 
from an artist who proposes to illustrate poetry is that 
he should be himself at least a passive poet. The 
second reason is that many of the most charming things 
in a poem are of such a nature that they cannot be 
illustrated. Their merit lies in their elusiveness ; a 
certain vagueness is of their very nature. To make 
a picture of Satan's massive bulk as he ^4ay floating 
many a rood" is to reduce poetry to a more or less 
exact science. Whether we will or no, a picture lends 
itself to drawing to scale. 

Minds of fine calibre usually object to illustrations 
in both poetry and fiction. The artist interferes with 



342 EXPOSITION AND ILLUSTRATION IN TEACHING 

their freedom. The influence of the fait accompli is 
powerful in all departments of life, but nowhere is it 
more powerful than here. After seeing a picture of a 
character in a novel, it is very difficult indeed to con- 
ceive of that character under a different face. Strongly 
imaginative visuals have usually invented for them- 
selves a very clearly defined picture of each of the 
characters of a story, and of characters in history whose 
faces have not been handed down to us. Such persons 
resent any picture that is not theirs. They say that 
this picture is not like the character, that is, is not like 
the picture they have formed in their minds. 

But, on the other hand, there are many who are unable 
to form a mental picture corresponding to a descrip- 
tion. These welcome illustrations, and all they demand, 
is that the illustration shall correspond to the facts 
contained in the text. This very simple demand is far 
less frequently complied with than one would expect. 
Authors have a standing grievance against artists for 
blundering in their representations of the matters dealt 
with in the text. The author makes the prisoner gaze 
gloomily at the four tiny squares of sunlight that the 
prison window allows to fall upon the opposite wall, 
and the artist represents nine tiny squares. The au- 
thor complains that the artist has not read the book 
with sufficient care. On the other hand, the artist 
often complains of the carelessness of the author. An 
artist friend of mine had the satisfaction lately of writ- 
ing to an author that if a certain character were to 
be depicted as doing what the author said he did, it 
would be necessary to draw the character with an arm 
twenty feet long. Indeed, it is mainly in connection 
with illustrations that discrepancies between different 



THE PICTURE AS ILLUSTRATION 343 

parts of the text are exposed. Of the two the author 
has the safer position. He raay, and frequently does, 
make a sUp in his topography without anyone being a 
bit the wiser. A careful examination of the work of 
almost any popular writer of fiction will show up some 
inconsistencies that have never been found out by the 
public, because the different parts are not confronted 
with each other. This confrontation is frequently 
forced on by the artist, whose work naturally gives itself 
over to criticism of this kind. 

An interesting parallel may be drawn between the 
concept and the image, on the one hand, and the 
author-picture and the artist-picture, on the other. 
As the concept has the power of crystallising out into a 
definite image, so the author-conception of the group- 
ing of elements may be crystallised out into the picture 
of the artist. 

The artist stands between the author and the 
reader. By means of words ideas pass from the author 
to the reader. So far as these ideas are capable of 
pictorial representation, they may be very vaguely set 
forth in the author's mind, and as vaguely m the minds 
of many of his readers. Some of the readers may have 
a much clearer and even more accurate picture than the 
author himself. So long as there is no flagrant contra- 
diction between the author-picture and the reader- 
picture, the two may exist comfortably side by side with- 
out either author or reader being aware how different 
the two pictures are. This agreement in difference is 
possible only because there is no objective standard to 
which both pictures may be referred. The moment the 
artist comes along, his picture supplies the missing 
standard, and both author and reader are able to com- 



344 EXPOSITION AND ILLUSTRATION IN TEACHING 

pare their picture with this external standard. Very 
often the artist's picture corresponds neither to the 
author's picture nor to any of the pictures formed by 
the readers. Indeed, it would be very wonderful if the 
artist's picture did coincide at all points with any other 
picture. On the other hand, in the case of a careful 
and skilful artist, there will probably be no justifiable 
difference between the author's account and its transla- 
tion into terms of space. Each reader will probably 
say, ^^Well, it is not just what I thought it would be, 
but it is quite in keeping with what the book tells us, 
so I suppose it's all right." It sometimes happens, 
indeed, that a reader of exceptional experience may have 
a truer picture than either the author or the artist, 
if by truth we mean fidelity to things as they really are. 
An author, for example, lays the scene of his story in a 
country that he has never visited. He has carefully read 
up his subject, and has acquired quite a store of second- 
hand local colour. The book is illustrated by an artist 
who also has never visited the country, and the illustra- 
tions are quite satisfactory to the author, who has no ob- 
jective standard by which to test them. On the other 
hand, a reader who knows the country in question might 
read the unillustrated book with pleasure and under- 
standing and never suspect that its author had no first- 
hand knowledge of the country, for this reader would 
interpret all that was said in terms of his own experi- 
ence,^ and would form for himself correct pictures with- 

^ An excellent illustration of what goes on unconsciously in the 
mind of such a reader is to be found in the twenty-ninth chapter of 
Ivanhoe, where the wounded knight consciously and deliberatel}^ inter- 
prets what Rebecca tells him about the doings of the besiegers of 
Torquilstone Castle. 



THE PICTURE AS ILLUSTRATION 345 

out suspecting that they did not correspond to what had 
been in the author's mind. Naturally, if the author 
goes into detailed descriptions, he is almost sure to 
betray himself to the reader who really knows, but he 
has at least a chance of getting off undetected, and I 
have known several cases in which such an author has 
been quite successful. But so soon as an illustrated 
edition falls into the hands of the specially well-informed 
reader, discrepancies are at once detected. 

It is much easier to hide one's ignorance in writing 
than in drawing. No doubt if a manuscript by an 
author depending upon second-hand knowledge is 
submitted to minute analysis by a person well versed at 
first hand in the matter described, it is almost impossible 
for it to stand the test. But the artist is in a much 
worse case. He plays with his cards on the table. He 
has a certain space that he must fill somehow or other. 
No doubt he is able to arrange matters so as to hide a 
certain amount of his ignorance. He may so place his 
figures that certain portions of their attire or accoutre- 
ments are not seen ; he may foreshorten certain lengths 
of which he is not sure, and make the laws of perspective 
responsible for any apparent discrepancy; above all, 
he may vaguely suggest certain possibilities, and leave 
the observer to fill in details at his own responsibiUty. 
This last method, transferred to the realm of letters, is 
that adopted by the ordinary author. In any case the 
worker in words is not called upon to describe any- 
thing he wishes not to describe. He is at liberty to 
select for description whatever pleases him. The 
artist, on the other hand, must meet his difficulties. He 
cannot merely omit them; and when he seeks to evade 
them, he has to do so in a way that is easily detected. 



346 EXPOSITION AND ILLUSTRATION IN TEACHING 

In a certain sense the artist may be said to be called 
upon to do the necessary elaboration of the author's 
meaning. It may be enough for the author to remark 
that there was a cupboard in the corner. He need not 
concern himself about what sort of cupboard it is; but 
the artist must make it some definite kind and shape 
of cupboard. He must, in fact, elaborate the idea. 
Some artists go in for far more detail than do others, but 
in every case they must go into greater detail than the 
author, wherever space relations are involved. Certain 
artists show great skill in giving just the right amount 
of detail, and in suggesting the rest. Others lean rather 
to the methods of Walt Whitman, and provide a series 
of elements in their spatial relations so that the content 
of the description may be made out without any effort 
on the part of the spectator. 

Since young people are necessarily in need of as much 
detail as can be communicated to them without undue 
strain, there can be no harm in using pictures copiously 
in teaching. Naturally, it is desirable that the idea of 
the picture as a whole should be the true idea, so that in 
the future the pupil may not have to unlearn anything. 
The exceptionally capable pupil may occasionally re- 
sent the restraint on his imagination imposed by the 
artist's work. But the average pupil, so far from 
resenting the artist's guidance, feels grateful for combi- 
nations of ideas that he could not have made for him- 
self. Not only does the picture supply combinations, 
it gives the elements as well. By the very fact that the 
artist is compelled to fill his space, he has to introduce 
many details that do not appear in the text at all. It 
would be intolerably tedious to state in writing a great 
many things that the artist can represent by a few 



THE PICTURE AS ILLUSTRATION 347 

strokes. It is easy for the artist to depict in a few 
square inches of book space what would take pages of 
descriptive writing to set down in a much less effective 
way. Further, it is much easier for the pupil to interpret 
the picture than the text. By a mere glance he gathers 
in a harvest of the eye that could hardly under any 
circumstances be gathered from reading. It is a 
healthy sign that teachers are now paying great atten- 
tion to the pictures in the text-books. Formerly, it 
was assumed that the pictures were the children's 
affair; they were regarded as mere attractions, things 
to please the pupils. Now teachers use the pictures as 
an integral part of the lesson. In many cases, indeed, 
the picture becomes the core of the lesson. In com- 
position, for example, a picture is often chosen as the 
basis of a story or explanation. But this is obviously 
not a case of illustration. The picture is being used 
for its own sake, and not in relation to something else 
upon which it casts light. Frequently a picture that 
was meant by the artist to illustrate one thing may be 
used by the teacher to illustrate another. Such pic- 
tures as " The Derby Day '' and '' The Railway Station,'' 
that were meant by the painter (W. P. Frith, who, by 
the way, began his career as an illustrator of the Eng- 
lish classics) to illustrate the humours of his time, may 
be used by the teacher as illustrations of the dress and 
general background of English life in the middle of last 
century. 

We have seen that all pictures are more or less ab- 
stract. As a matter of fact, we may arrange pictures in 
a regular series of classes of ever increasing abstract- 
ness, till in the final resort we reach a stage that is not 
really pictorial at all, but diagrammatic. It is impos- 



348 EXPOSITION AND ILLUSTRATION IN TEACHING 

sible to draw a hard and fast line between the picture 
and the diagram, for there is really a long series of de- 
grees of abstractness from the all but complete repre- 
sentation of an actual object or scene at the one end, 
to the complete reduction to one class of relations at 
the other. 

The necessary and sufficient mark of the picture is 
that it seeks to reproduce the object as it appears to the 
eye. The diagram, on the other hand, isolates certain 
relations, and by isolating emphasises them, and thus 
frees them from complication with others. Generally 
speaking, the picture may be said to deal with things 
as they appear, the diagram with things as they are. 
The picture works by appealing to suggestion; the 
diagram seeks to eliminate suggestion altogether, or, if 
it makes use of suggestion, limits it strictly to one 
particular line of action. 

The abstractness of an ordinary picture is made clear 
when we consider the conventional element in drawing 
and painting. We are apt to think that what we call a 
true reproduction of nature necessarily conveys to the 
human mind the impression of the original. To many 
it seems superfluous to write and publish such a book as 
Mr. Robert Clermont Witt^s How to Look at Pictures, 
But here we have 160 large pages of print explaining 
what is usually taken for granted. Pictures are gener- 
ally supposed to be self-interpreting, at any rate in so 
far as they reproduce scenes or objects from the real 
world. Yet, leaving out of account the technicalities 
of the schools, there remains the fact that we have in 
the most literal sense to learn how to look at pictures. 
Psychologists have found that illiterate and savage 
people do not at all understand what is meant by a 



THE PICTURE AS ILLUSTRATION 349 

given picture. They have a grain of salt for the story 
of the Greek artist Zeuxis, who painted some cherries 
so naturally that the birds came and pecked at them. 
In the case of the savages of Borneo, it has been found 
that they do not recognise the portrait of a man as a 
man at all, to say nothing of being a likeness of a par- 
ticular man/ It is clear that we read into our pictures 
more than is actually there. 

The picture-maker must vary his method according as 
his purpose is to give aesthetic satisfaction or to impart 
knowledge. It is, of course, possible for a picture to do 
both; but for purposes of illustration the informative 
side is of more consequence. So soon, however, as the 
purely informative aspect dominates, there is a danger 
of serious damage to the other. A glacier painted by 
an artist for his own satisfaction and the pleasure of 
his patrons is a very different thing from the glacier 
painted to illustrate a geological lecture. When Mes- 
sieurs Lecerf and Petit let themselves loose on their 
cartoons for teaching La Morale par Exemple ^ the ar- 
tistic conception and execution are hardly worthy of the 
fine lessons they teach. On the other hand, it is quite 
possible for the artistic sense to have too free play for 
the results to have any informative value. Such illus- 
trations as those of Cruikshank have no doubt an 
illustrative value. They illustrate the spirit of the 
text. They owe whatever charm they possess to their 
whimsical suggestiveness. But on the informative side 

^Dr. C. S. Myers tells me that this does not apply to the higher of 
the two grades into which the Borneans whom he has studied are 
clearly classifiable. See also G.J, Romanes : Mental Evolution in 
Man, p. 188. 

^ Collection publiee sous la direction de M, Edouard Petit, Inspecteur 
Gineral de V Instruction Publique. 



350 EXPOSITION AND ILLUSTRATION IN TEACHING 

they are worse than useless. The figures are unnatural, 
not to say impossible. But the reader is willing to 
accept them in connection with a certain class of book, 
and to interpret the text by their means. They are a 
sort of humorous diagram. We feel that if they have a 
place anywhere it is in the pages of Dickens; in Scott 
they are objectionable. 

On the purely informative side, illustrative pictures 
leave as little as possible to the mind of the observer. 
Suggestion must be called into play; but only the 
most obvious suggestion is used. The real is not here 
sacrificed to the phenomenal. The illustration of ad- 
vertisement gives examples of this sort. At any of our 
railway stations may be seen pictures of the removal 
vans used by various firms. In most cases the vans 
are drawn in an impossible position. They are repre- 
sented with their long sides parallel to the picture plane, 
which is very convenient, since the printing on the sides 
of the van can thus appear exactly as in a book, without 
the disadvantage of foreshortening. On the end of the 
van, naturally, the printing should appear to vanish 
towards the centre of vision. The advertisers probably 
are perfectly aware of this, but as foreshortened print- 
ing is not so emphatic as the straightforward kind, they 
prefer clearness of printing to accuracy of drawing, 
and simply represent the end of the van as if it also were 
parallel to the picture plane. No great harm is done. 
The ordinary observer is not at all concerned with the 
breach of the rules of perspective. This I have tested 
by more than one hundred separate enquiries. Experi- 
ence shows that, when questioned as to whether there 
is anything wrong with the poster, the ordinary intel- 
ligent observer makes some comment or other, either 



THE PICTURE AS ILLUSTRATION 351 

about the kind of printing, the colour of the poster, or 
the removal-conditions quoted, — all of which is a full 
justification of the practical wisdom of the advertiser, 
whose business it is to remove furniture and not to 
educate the public. Obviously, the teacher must take 
another view. 

This desire to combine the picture element with 
the diagrammatic has led to the invention of the iso- 
metric mode of projection. The draughtsman wishes 
to suggest the appearance of the object as a whole, 
and yet does not want to give up the advantage of 
drawing to scale and making measurements from his 
drawing. Accordingly, he has hit upon the plan of 
drawing all his horizontal lines at an angle of thirty 
degrees with the horizontal edge of the paper, and thus 
always presenting a corner projection of the object in 
such a way as to look not altogether unlike the real 
object, and at the same time to allow the draughtsman 
to make measurements on and from his drawing. 

The compromise here effected in the interests of 
utility is paralleled by a compromise effected in the 
interests of art in the Eastern monumental reliefs. 
The Assyrian Bulls, if looked at full in front, show up a 
pair of forelegs, just as we would find if we viewed a real 
bull from this standpoint ; and if the relief is looked at 
from the side, four legs are seen, just as would be the 
case if we observed from the side a bull in the act of 
walking. If, now, the observer takes a mean advantage 
of the old sculptor and looks at the relief bull from a 
point midway between the front and the side, he sees 
the animal with five legs. As an informative illustration 
this bull is a failure, but as an artistic production it has 
the advantage of preserving the illusion of naturalness 



352 EXPOSITION AND ILLUSTRATION IN TEACHING 

from the two most important points of view, the front 
and the side. 

The pictorial series, in order of increasing abstract- 
ness, may be thus summarised : — 

(1) Reahstic pictures in which nothing is left to the 
imagination but the work of combining the elements 
supplied, i.e. in interpreting the lines and colours ac- 
cording to the ordinary conventions, so as to call up 
the impression of the actual object or scene. 

(2) Conventional pictures in which the elements 
must be combined according to a more or less arbitrary 
but intelligible convention. To this class belong ex- 
amples of the more outre schools of painting that 
require special training to understand. Lead glass 
work in ecclesiastical decoration would clearly belong 
to this class. 

(3) Diagrammatic pictures in which various more or 
less mechanical conventions are recognised. To this 
class belong such drawings as those worked on the iso- 
metric system, or any similar, recognised system. 

(4) Diagrams in which the drawing is not in the 
ordinary sense quite like the object represented, but 
corresponds to it in certain points. Plans and eleva- 
tions, for example, are not really like the objects, and 
yet as they correspond to them in space relations they 
may be said to resemble them. To this class also be- 
long all manner of maps, and that large class of draw- 
ings that in biological and other scientific text-books 
are labelled '^ diagrammatic." These drawings retain a 
certain resemblance to the original objects, but the 
draughtsman has taken the liberty of suppressing what- 
ever elements he has found it inconvenient to intro- 
duce. The main purpose of this kind of diagram is to 



THE PICTURE AS ILLUSTRATION 353 

divide and conquer. In dealing with the vascular 
system, for example, it is a positive disadvantage to 
have the diagram loaded up with details of the nervous 
system. There is a place for the nervous system by 
itself, and also along with the vascular. But this com- 
bined presentation belongs to a different stage of teach- 
ing. This class of diagram does suggest the real ap- 
pearance of the objects represented, but only in a vague 
way. The vagueness is no disqualification, for the 
general appearance of the object is not at this stage 
important. 

(5) The final stage is reached when we come to those 
diagrams in which we have one fact represented by 
another with which it has no apparent connection. 
The two are wholly disparate, save in respect of the 
one element in which they are compared. There is no 
connection, for example, between a straight line and 
the amount of wool exported from Australia, and yet 
the varying state of the export trade in wool may be 
well illustrated by a series of lines of different lengths. 



2a 



CHAPTER XY 
The Diagram 

The relation between the picture and the diagram 
as means of illustration may be brought out by a 
consideration of the relation between the easy and the 
simple in teaching. These two terms are sometimes 
taken to be synonymous. But everything depends 
upon the stage the pupils have reached in the subject 
under discussion. We have seen that while a generalisa- 
tion is simpler than the mass of details from which it has 
been drawn, it is easier only to those who have mastered 
the details, and thus earned their generalisation. So 
with graphic illustration. Speaking generally, the dia- 
gram is simpler than the picture, and yet the picture 
is in most cases easier than the diagram. If we follow 
the principle from the simple to the complex, it would 
seem that we ought to begin with the diagram and rise 
to the picture. The teacher, however, is driven to 
reverse the process, if only to be consistent with the 
other teaching principle, from the concrete to the 
abstract. We have here a practical example of an only 
too prevalent tendency to pit one principle against an- 
other in an unintelligent way. So soon as we take a 
wide enough view, we find that the two principles are 
quite consistent. 

In point of fact, the place of the picture is both at the 
beginning and the end of a process of teaching. At the 

354 



THE DIAGRAM 355 

beginning it gives a general idea of the whole with 
which we are dealing. This can be grasped in a more 
or less vague way. There then ought to follow a study 
in greater detail, in which certain elements have to be 
treated by themselves. Here the diagram is obviously 
in place, and may be used with whatever degree of 
abstractness is required. When the detailed study has 
been completed for that particular stage, the picture 
should once more be introduced to gather up the pupil's 
new knowledge and fit it into its proper place. In each 
teaching unit involving graphic illustration we should 
begin with the picture, and end with the picture. All 
between is the domain of the diagram. 

Yet so strong is the power of the picture that it 
remains immanent throughout the process, and is ready 
at any moment to obtrude itself. A diagram seems to 
have an inherent tendency to acquire content and 
become a picture. Since the value of the diagram is 
its abstractness, it is clear that a loss of abstractness 
is a loss of the virtue of the diagram as such, except in so 
far as the pictorial element is consistent with the dia- 
grammatic. The general sense of the solidity of the 
heart that obtrudes itself upon the flat diagrammatic 
representation of it does not in any way hinder the 
diagram in its illustrative work. But if we are dealing 
diagrammatically with a question of quantity, and the 
picture element introduces the question of quality, 
the pictorial influence is prejudicial. 

This is well shown in some of the popular methods of 
diagrammatic representation. It is now fashionable to 
represent quantities pictorially rather than diagram- 
matically in the strict sense of the latter term. For 
instance, it is desired to convey a vivid impression of the 



356 EXPOSITION AND ILLUSTRATION IN TEACHING 

amount of tobacco smoked in his lifetime by a man who 
consumes so many cigars per week. This is supposed 
to be best represented by a drawing in which the cigar 
bears the same ratio to the man that the weight of to- 
bacco consumed during the man's hfetime bears to his 
own weight. Accordingly, a manikin is represented 
with an enormous cigar in his mouth. No doubt the 
area of the cigar, as represented by square centimetres, 
has the same ratio to the area of the man in the same 
denomination as the number of pounds of cigar has to 
the number of pounds of man. But while we have thus 
an appearance of mathematical accuracy, the only 
effect produced upon the observer is the impression 
that the man smoked a very great number of cigars. 
On the whole, the statement in words of the number of 
pounds of tobacco and the number of pounds the man 
weighed would convey a clearer idea of the situation 
than the diagram does. It is commonly said that the 
illustration is much more interesting when put in the 
pictorially diagrammatic way. But the gain in interest 
is at the expense of relevancy. The sizes of the armies 
of Europe may be represented by a series of soldiers 
dressed in the uniform of the respective countries, 
each soldier being made of a certain size, according to 
some standard, so as to represent the size of the army 
of his country. The resulting impression is not at all 
clear. It is complicated in two ways. 

In the first place, we have the introduction of quality 
where it has no place. While we are considering the 
size of the armies of Russia and Italy, we have nothing 
to do with the peculiar cast of countenance of a Russian 
or an Italian; yet these qualities are thrust upon our 
notice in the drawing. No doubt the appearance of the 



THE DIAGRAM 357 

men, their uniforms, and their weapons are of the utmost 
consequence in considering the value of the various 
armies. But this particular diagram is used to illus- 
trate only the one element of size. The rest may be 
illustrated in various ways. Some parts of the whole 
illustrandum may be best represented pictorially, as, for 
example, the weapons and accoutrements; but wherever 
statistical elements alone are involved, the pure diagram 
will be found to be most serviceable, and least apt to 
convey false impressions. 

The second source of complication in the pictorial 
diagrams is the introduction of the element of area. 
If the mere height of the soldiers represents the size of 
the army, then clearly a series of straight lines would, 
for illustrative purposes, serve better than the pictured 
figures. But if the numerical proportion of the armies 
to one another is represented by the area covered by 
the figure of the soldier, then a very serious difficulty is 
introduced. The ordinary reader can compare straight 
lines with very little difiiculty. But the comparison of 
areas is beyond him. Anyone who has not given the 
matter attention will be surprised at our general weak- 
ness in estimating area. We are all singularly feeble 
in the matter of comparing the relative sizes of surfaces, 
and in particular in correlating lengths with areas. 
We can compare two lines with each other with a fair 
chance of justly estimating their ratio, but few among 
us can make even a reasonable guess at the relative 
areas of two given circles or squares. To prove how 
easily we may be misled in comparing lines with areas, 
ask any friend who has not had the experiment already 
imposed upon him how many cent pieces or ^'pennies" 
we can place flat on the surface of a silver dollar without 



358 EXPOSITION AND ILLUSTRATION IN TEACHING 

any one of them overlapping, however slightly, the cir- 
cumference of the larger coin. The ordinary answer 
varies from three to five. The fact, however, is that 
even two of the little copper coins are more than the 
dollar can receive on its surface under these conditions. 




Fig. 5. 



Take two small coins, say quarters, and place them on a 
table at such a distance from each other as you think 
will leave room for one other quarter to fit in exactly 
between the two. When you have tested your result, 
you will probably find that you are considerably wrong 
in your calculation, and that any friend with whom 
you experiment goes wrong in the same direction as 
yourself. You are really trying to determine the length 
of the diameter, but the area of the coin leads you into 



THE DIAGRAM 359 

error. Our weakness is shown also in our inability to 
guess correctly without previous practice the height in 
inches of a silk hat resting on its crown. Further, take 
two pieces of paper and, putting the one above the other, 
cut out in duplicate the shape indicated in figure 5. 
You will then have two pieces of paper of exactly equal 
area, but if you place them one below the other, as in 
figure 5, you will find it very difficult not to maintain 
that the lower of the two is greater than the upper. 

Psychologists supply us with many examples of false 
impressions conveyed with regard to areas, lengths, 
and directions, and one would almost think makers of 
diagrams deliberately selected modes of representation 
that illustrate certain of the psychologists' illusions.* 

It is customary to represent the areas of countries 
and continents by a series of squares or triangles; and 
at first sight it may appear plausible to maintain that, 
since we are illustrating areas, the best illustration is 
surely other areas. It may even be asked, if we cannot 
compare intelligently little areas, like printed triangles 
and squares, what hope is there that we can compare 
areas like those of continents and countries ? Now it 
has to be admitted frankly that most of us have no real 
conception of what is meant by the hundreds of thou- 
sands of square miles that we read about in our geog- 
raphy text-books. But it is one thing to know a mat- 
ter absolutely, and another to know it relatively. It is 
one thing to know what is meant by the statement that 
North Carolina contains 52,250 square miles, and an- 
other to realise that its area is a little over twenty-five 

^ Lightner Witmer, in his Analytical Psychology, Chap. Ill, par- 
ticularly pp. 86-98, gives some exceedingly interesting, and from the 
teacher's standpoint most instructive, illustrations. 



360 EXPOSITION AND ILLUSTRATION IN TEACHING 



times that of Delaware. We may not be able to realise 
the vast extent of country implied by these figures, but 
we may be able, by comparison with a smaller state (in 
this case Delaware) with which we are assumed to have 
a much better acquaintance, to make certain practical 
applications of the statement of the larger area. If we 
have a standard area^ that we really know by having 
walked or driven over great parts of it, we may on that 
basis build up a scale which we can intelligently use. 
The bigger the available unit the better. An additional 
advantage follows when the pupil is able to compare 
by actual inspection a smaller unit than his standard, 
so as to determine how many times this smaller unit is 
included in the standard unit. If, for example, in this 
particular case the pupil who lives in Delaware has had 

a chance of running 
over Rhode Island, 
which has more than 
half the area of Dela- 
ware and Connec- 
ticut (more than 
double the Delaware 
area), he will find his 
standard (Delaware) 
much more useful 
for purposes of com- 
parison. 

But granting the 
standard, there re- 
mains the question of the best means of graphically 
representing the unit and its multiples. Here the text- 
books are again in favour of reduced areas. North 

1 See p. 315. 



T r 

Fig. 6. 



THE DIAGRAM 



361 



Carolina is represented by a square of, say, 2j-inch 
side, and in the corner the area of Delaware is repre- 
sented by a square of |-inch side. If the two squares 
are left thus, they do 



Fig. 7. 



not give a very clear 
impression of the rela- 
tive sizes of the two 
states. It is found by 
experiment that a class 
gets a better compari- 
son between the two 
squares in figure 6 if 
the sides of the larger 
square are marked off 
into five equal parts, 
and still better if the 
whole square is marked off into twenty-five squares 
of the Delaware size, as in figure 7. 

From the ordinary atlas the pupil is apt to get a dis- 
torted view of the relative sizes of the countries of the 
world. Each country and continent has a map to itself 
on a sheet of its own, so that North America, Germany, 
and Scotland all appear to be of the same size, the 
only help the pupil gets being the little scale of miles 
that he is very apt to overlook. Wall maps have the 
same defect. Some publishers adopt the reasonable 
plan of inserting in the corner of maps that are drawn 
to a very small scale a little outline map of some stand- 
ard country drawn to the same scale. Thus, the state 
in which the pupil lives might well appear in the corner 
of maps of the continents, India, China, Australia, 
and the United States. To illustrate the relative sizes 
of the countries of Europe an ingenious teacher first 



362 EXPOSITION AND ILLUSTRATION IN TEACHING 



Comparative View of the Areas 
OF THE Continents, Reduced 
TO Squares. 



made a tracing of the whole continent from the wall 
map, then he coloured each of the countries with a flat 
wash, next he cut out all the countries and mounted 
Russia on a sheet of paper that just comfortably re- 
ceived it. After this he got a series of sheets of paper 

of the exact size used 
to mount Russia, and 
pasted on each of them 
one of the other coun- 
tries of Europe. The 
amount of white margin 
in the case of small coun- 
tries like Denmark and 
Belgium certainly em- 
phasised their relative 
poverty of area. 

The accompanying 
diagram,* figure 8, rep- 
resents an attempt to 
illustrate the areas of 
the continents. It is 
found in practice to be of very little service. In order 
to test its utility, I experimented in several towns with 
many classes of pupils of various ages from 12 upwards. 
The area of one of the continents was given, and the 
problem set was to estimate from the diagram what the 
areas of the other continents were. The answers were 
very wide of the mark, and certain interesting varia- 
tions were observed. The worst results were obtained 
when the area supplied was that of Australia; the next 



AFRICA. 




NORTH AMERICA 




> 


SOUTH AMERICA 




1 

H 
I 
> 

S 
m 

33 


EUROPE 




I 
> 

> 






m 

c 


AUSTRALIA 





Fig. 8. 



* John Macturk: Elementary Physical Geography, p. 317. 
2 Reproduced by kind permission of Messrs. William Collins, Sons 
and Co., London and Glasgow. 



THE DIAGRAM 



363 



worst when Asia was the standard; the best results 
followed when either North or South America formed 
the starting-point. Classes that had studied mensura- 
tion did better than those that had not. I was able 
to eliminate the difference in age, for I managed to get 
four classes of boys of the same age, two of which had 
studied mensuration and two had not. A further pecu- 
liarity was that when the diagram was put in the form of 
a series of six squares standing outside of each other, and 
arranged in order of size, the results were better than 
when the squares were so placed as to have one angle 
common. The explanation is probably that when the 
squares were superimposed there was greater '^ interfer- 
ence '^ in the sense that term bears when used in physics. 

Conspicuously better results were obtained when two 
of the six areas were given, the best results of all being 
obtained when Europe and Africa were the continents 
selected as standards, though Asia and Australia made 
a combination that had results very little inferior. 

In point of fact, however, the following table that 
accompanies the diagram in Mr. Macturk^s book gives a 
more useful presentation than does the diagram: — 



Size of 


THE Continents (including Islands)* 




Greatest 


Greatest 


Area in Sq. 


Comparative 




Length 


Breadth 


Miles 


Size 


Europe . . . 


3400 m. 


2450 m. 


3,700,000 


1 


Asia .... 


6700 m. 


5400 m. 


16,400,000 


^ 


Africa .... 


5000 m. 


4600 m. 


11,100,000 


3 


N. America . . 


5600 m. 


3120 m. 


7,600,000 


2 


S. America . . 


4500 m. 


3000 m. 


6,800,000 


H 


Australia . . . 


1900 m. 


2400 m. 


3,000,000 


■ 1 



^ Take Europe as the standard of comparison. 



364 EXPOSITION AND ILLUSTRATION IN TEACHING 

In the table the areas are given in sufficiently round 
numbers to admit of easy comparison with each other, 
a comparison that is further aided by the ^'compara- 
tive size" column. It would be well, however, as a 
matter of presentation that the continents should be 
arranged in the table in regular ascending or descending 
order of size to match the diagram. Taken along with 
the table, the diagram may be said to be helpful; but 
if the teacher has to choose between the comparative 
size column and the diagram, he will be well advised 
to give up the diagram. The illustrandum being the 
column of ''area in square miles,'' the comparative 
size column will certainly be a better illustration than 
is the diagram. When a class is confronted with the 
squares in figure 8 without any indication that they 
represent continents, the pupils are found to be inca- 
cable of estimating the relative areas of the squares. 
Given the area of the Europe square as 100, only 
two out of a class of 75 postgraduate students esti- 
mated with reasonable correctness the areas of the re- 
maining five. Eighteen of them estimated the largest 
square as between 700 and 800. The general impres- 
sion produced by the students' estimates was that the 
diagram by itself confused rather than helped. 

Still less hopeful is the accompanying diagram, figure 
9. The wider circle has an area one hundred times as 
great as has the small black circle in the centre. As 
the total area of the United States, including Alaska, 
is 3,617,384 square miles, and the area of Indiana is 
36,350 square miles, the diagram might be used to illus- 
trate the relation between the area of this state and the 
area of the whole republic. The diagram is supposed 
to make the ratio clearer than does the mere statement 



THE DIAGRAM 365 

of the figures. As a matter of fact, the statement that 
the one area is almost exactly a hundred times the other 
conveys a much clearer idea than does the presentation 
of the diagram. Pupils are unable to estimate the 
ratio between the two circles. I have made this the 




Fig. 9. 

subject of experiment by placing a large copy of the 
diagram drawn to scale before about thirty classes of 
pupils between 12 and 15 years of age (representing 
altogether 1245 individual pupils) without giving any 
hint about what it represented geographically. The 
only question asked was: How many times is the big 
circle bigger than the little one? I made the same test 
with various classes of undergraduate students (453 in- 



366 EXPOSITION AND ILLUSTRATION IN TEACHING 

dividual students in all) of ages 19 to 22. The follow- 
ing is the percentage results of the estimates formed 
by the various pupils : — 





Group I 


Group II 


- 


Pupils 12-15 


Pupils 19-22 


Under 100 

Exactly 100 

Over 100 


56.2 

15.7 

28.1 


30.1 
29.0 
40.9 




100.0 


100.0 



Naturally the older pupils made fewer wild guesses 
than the juniors. In Group 1, 17.2 per cent estimated 
the area as under 20 times; in Group II, only 2.3 per 
cent made this low estimate. But strangely enough, 
while of Group I only 8.0 per cent estimated over 300 
times, 9.3 per cent of Group II made this exaggerated 
estimate. One striking difference between the two 
groups is that there is much more ^^ round number" 
work among the first Group. The second Group quite 
obviously deals with squares of numbers, while the first 
Group have exactly 50.7 per cent of even number guesses 
— i,e, 20, 30, 40, . . . 200, 300, 400, etc., up to 1000. 
In Group I 2.5 per cent estimate exactly 1000. Only 
one student in Group II makes this loose guess. In the 
first Group one pupil guesses 5000, and one actually 
goes the length of 10,000. The great majority of the 
guesses are, in fact, quite wild. About a dozen pupils 
in Group I give such inexplicable answers as ^^They are 
as big as each other.'' But a good many must have 
thought what one pupil had the courage to write: 



THE DIAGRAM 367 

'^One cannot tell how much bigger, as the small one can 
go into it almost as many times as one likes/' 

In the case of Group II it appears likely that 29 per 
cent represents the real proportion of those who esti- 
mated 100 correctly. The same can hardly be said 
for Group I. The tendency to select round numbers 
is so marked that we must make allowance for the in- 
clination to be specially attracted to 100 because it is 
so preeminently a round number. Thus, while 15.7 per 
cent guessed 100 exactly, no fewer than 12.04 per cent 
guessed 50 exactly, while 5.5 per cent guessed 200 
exactly. 

The important result of the experiments from the 
point of view of Illustration is that the diagram gives 
no real help in estimating the relative sizes of two geo- 
graphical areas. Can it be maintained that the illus- 
tration works the other way? If the pupils are unable 
to estimate that the big circle is a hundred times bigger 
than the little one, are they at all likely to be clearer 
about the ratio of 1 to 100 by looking at the diagram 
after being told what the ratio is? If not, can the dia- 
gram be said to serve any useful purpose? The answer 
would appear to be that, taken in connection with the 
actual figures, there may be a certain aesthetic satis- 
faction in seeing the diagram. It may therefore help 
in fixing an impression that is made by other means, 
but its effect must be recognised to be aesthetic, not 
didactic. 

Geometricians discriminate between what they call 
diagrams of illustration and metrical diagrams. The 
first kind 

" are intended to help the reader to follow the mathematical rea- 
soning. The construction of the figure is defined in words so 



368 EXPOSITION AND ILLUSTRATION IN TEACHING 

that even if no figure were drawn the reader could draw one for 
himself." ' 

The second kind are 

"employed in an entirely different way — namely, for purposes 
of measurement. The plans and designs drawn by architects and 
engineers are used to determine the value of certain real magni- 
tudes by measuring certain distances on the diagram. "^ 

The diagrams we have just been dealing with must 
be regarded as more or less illegitimate examples of the 
metrical kind. No doubt they are used to illustrate 
certain relations, and these relations are of a purely 
quantitative nature. On the other hand, they are not 
set out so that measurements may be taken from them. 
No doubt we could calculate from them the relations 
they illustrate, but this is certainly not the function 
they were introduced to perform. Rather are they 
called upon to illustrate calculations that have already 
been made. They are, in fact, a hybrid between the 
two classes. 

In spite of the literal meaning, — ''marked out by 
lines," — the term diagram may be applied to drawings 
in which colour plays an essential part. The areas in the 
drawing may indicate one set of facts, while the colours 
that are washed in over the areas may indicate another. 
The areas may, for example, indicate quantitative re- 
lations, the colours qualitative. In a geological map 
the extent of the various strata is indicated by the area 
set apart for each, while the nature of the strata is 

^ How far this is true of the ordinary reader may be tested by 
asking some one to read the Meno, 82-85, from a text without a dia- 
gram, and then make an illustrative diagram to suit. Few indeed will 
be able to supply what is wanted. 

2 J. Clark Maxwell, in the Ency. Brit., ninth ed. Vol. VII, p. 149. 



THE DIAGRAM 369 

indicated by the colours : hlack may indicate coal; yellow, 
chalk; red, volcanic rocks; and so on. It is to be noted 
that here we have another example of the immanence 
of the picture in the diagram. There is a natural con- 
nection between black and coal, and between red and 
the rocks that are produced by fire. The same feeling 
after the pictorial is seen in the maps illustrating the 
various levels of the different parts of the earth's 
surface. It is a natural convention to represent the 
low-lying lands by different shades of green according 
to their height, the higher mountainous levels by 
various shades of brown (points above the snow-line 
being left white), and the sea by varying shades of blue. 
But colours may be used in a completely abstract way, 
as in the case in which exports and imports are repre- 
sented by different colours. 

Sometimes colours and areas are combined for illus- 
trative purposes. When this is done, there should be 
the greatest care in maintaining consistency in the use 
of the colours. In a diagram lying before me as I write, 
there are two circles, each divided up into sectors 
representing the amounts of the imports and exports 
of Great Britain from and to various countries. Here 
each country should retain the same colour in both cir- 
cles. But I find that France is green in the imports 
and salmon-coloured in the exports ; Holland is salmon- 
coloured in the imports and blue in the exports ; Russia 
is yellow in the exports and blue in the imports. It 
may be thought that change in the colours is a trifling 
matter; but somehow colour has a great attraction for 
all of us, and particularly for young people. Nothing 
can be called trifling that draws attention in the wrong 
place and suggests difference where none exists. 

2b 



370 EXPOSITION AND ILLUSTRATION IN TEACHING 

A favourite method of representing statistical facts is 
by means of columns of varying height. The method 
is excellent, but it must be used with certain restrictions. 
First, the element of area must be eliminated. The 
columns must be of uniform width, so that the real 
measurement is made in height. In several diagrams 
I have examined I have found that when very large 
numbers have to be used along with small numbers, the 
columns representing the bigger numbers are so tall that 
it is impossible to include them in the page. Accord- 
ingly they are broken up into strips and placed side by 
side. No objection need be taken to this so long as 
the strips are of uniform length. Six such strips would 
naturally make a biggish rectangle, and would there- 
fore represent a very large number, but the largeness of 
the number would be estimated by the number of strips, 
not by the area of the rectangle. Sometimes the mis- 
take is made of representing a quantity that is just too 
big for a single strip by two equal strips, each a little 
bigger than half a standard strip. This is a blunder, 
for in this case we are driven to deal with area and not 
merely with length. The quantity should be repre- 
sented by a complete standard strip and a little bit of 
an additional strip. Each column is, in fact, treated as 
a line, and the complex diagram is really made up of a 
series of lineal measurements. We judge by the heights 
of the various columns, and thus get a good general 
idea of the comparative importance of the different 
quantities. When it comes to accurate details, we must 
fall back upon the actual figures, which are usually 
available. As a rule it is not wise to use illustrations 
of this kind as metrical diagrams. 

Psychologically, it is not quite accurate to say that 



THE DIAGRAM 371 

columns may be treated merely as lines. Our estimate 
of the width of columns is affected by the relative heights 
of the columns compared. A low column appears wider 
in proportion to a high column of the same real width. 
But this peculiarity need not interfere with the use of 
columns as illustrations of statistical relations in one 
denomination. So long as we have a standard height 
and a uniform width, we can treat them merely as thicker 
lines than usual. A particularly useful form of colum- 
nar diagrams is that in which squared paper is used as the 
groundwork, and squares are blackened so as to form 
columns of various heights. Each column is in this 
case so many squares high, and the ^^ permanent sug- 
gestion'^ of the squareness of the unit prevents the 
question of breadth arising; though it must be ad- 
mitted that in the case of a fraction of a square being 
filled up at the top of a column there is danger of a 
trifling disturbance through the breadth bias. 

While it is true that quantities are better represented 
by straight lines ^ than by areas, there is the limitation 
that when there is a great disparity between the two 
quantities compared, the mind may be unable to make 
the comparison. If, instead of the squares in figure 7, 
we draw a line one inch long to represent the area of 
Delaware, and another twenty-five inches long to 
represent North Carolina, it will be discovered that 
pupils find it impossible to make an accurate estimate 

^ In connection with the view that the straight line is the funda- 
mental form of quantitative illustration, my friend, Dr. William Gar- 
nett, the eminent physicist, refers to the fact that in physics all meas- 
urements are ultimately reduced divisions of a line. The galva- 
nometer, the thermometer, the barometer all exemplify this. Even 
in the balance the line remains the standard, though in this case it 
is reduced to zero. 



372 EXPOSITION AND ILLUSTRATION IN TEACHING 

of the relation between the two areas. In such cases 
the Hne must be broken up in some way, so that the 
ratio may be made manifest. One writer who wishes 
to represent by means of straight hues the ratio between 
the trade of the British Isles and the trade of the vari- 
ous British colonies, represents the British trade by a 
line so long in proportion to the others that he has to 
fold it into what may be described as a spiral rectangle 
that has rather more than two and a half whorls. 
Then this rectangle is filled with other lines variously 
folded. The perverted ingenuity of the plan may be 
gathered from its application in figure 10 to the areas 
of various states of the Union. The plain statement 
of the facts is : — 

Rhode Island 1,250 square miles. 

Maryland 12,210 square miles. 

Kentucky 40,400 square miles. 

New York 49,220 square miles. 

Illinois 56,650 square miles. 

Texas 265,780 square miles. 

This is contorted into 



TEXAS 



RHODE ISLAWD 



Fig. 10. 



THE DIAGRAM 373 

Two principles should be kept in view when we are 
dividing up a line so as to use it effectively in quantita- 
tive illustration. The first is that we should always 
work in multiples of the smallest line to be included. 
Thus, in the area-of-North-Carolina illustration (figure 
7, page 361), we should divide the twenty-five line into 
five lines, each five times the length of the line represent- 
ing the area of Delaware. Had we been dealing with 
the state of New York, which is almost exactly twenty- 
four times the area of Delaware, we would divide the 
longer line into four parts, each six times the Delaware 
length. Naturally, if there is not a convenient multiple 
to include all that we want without leaving anything 
over, than we must adopt the nearest multiple and 
represent the remainder by a proportionately smaller 
length. If the bigger state were represented by the 
number twenty-six (Arkansas, with 53,850 square miles, 
fits in here almost exactly), we might either take nine 
as the multiple and give two full lines and eight-ninths 
of another, or take five, as before, and add a fifth of an- 
other. 

The second principle is that we should arrange our 
rows of multiple lines horizontally rather than vertically, 
as it is found that the eye works more easily from side 
to side than up and down. 

It is probable that it is this difficulty in dealing in 
terms of straight lines with widely different quantities 
that has led to the introduction of illustrations by areas. 
These give a wider range, without the need of trouble- 
some foldings or duplications. Rectangular areas seem 
to lend themselves more readily to subdivision than do 
circular areas. But this does not prevent the enter- 
prising illustrator from using the circle. Indeed, this 



374 EXPOSITION AND ILLUSTRATION IN TEACHING 

form of illustration is at present rather in favour. A 
circle is taken to represent some total, and is divided 
up into various sectors, each representing a specific 
part of this total. But here, again, it is very difficult to 
estimate the areas of the sectors. The usual way is to 
make an estimate of the relative areas of the various 
sectors by comparing the parts of the circumference cut 
off by the including radii. Considerable skill in estimat- 
ing angular measurement may be acquired by a study 
of the face of the clock and the different positions of 
the hands. Limiting himself to the positions of the 
twelve hours, the student assumes the unit of the hour 
as equivalent to 30°, and by estimating the position 
of the radii in relation to the fixed points of the hours, 
he can make a fair guess at the number of degrees 
included, and therefore of the proportion of the area 
of the circle included in a given sector. 

The two following diagrams were published in an 




official document to illustrate certain quantitative 
relations. One would have thought that the percent- 



THE DIAGRAM 375 

ages required no help, but somehow the drawings were 
assumed to make the matter clearer, till one of the offi- 
cials, who had trained his eye on the clock-face 
standard, chanced to see them, and declared after a 
moment's inspection that both were incorrect (a) to 
the extent of two-thirds of an hour {i.e. 10°) and (6) 
to the extent of one-third of an hour {i.e. 5°). On 
measurement, the reader will find that the estimate is 
almost exactly right, so skilful is it possible to become 
at estimating angular measurement by reference to a 
fixed standard. It is true that this is not quite an 
estimate of areas, but rather of positions on a circle. 
The estimate of the included area is really an inference 
from the angular measurement. This last fact has 
probably something to do with the popularity of the 
circular form of quantitative illustration. 

Sometimes the circular diagram is used in a way 
that depends still less on the area-sense. The state of 
a particular business of some complexity, or of some 
government department, in a given year is represented 
by an inner circle. Each succeeding year is represented 
by an outer concentric circle, and the increase or dimi- 
nution in certain elements (sales, cases, prosecutions, 
deaths, or what not) is indicated by the protrusion of 
larger or smaller extensions of uniform shape, but vary- 
ing size, from the original circle. If the concentric 
circles increase by a uniform lengthening of radius each 
year, the protrusions from the original circle may be 
compared with each other on the same standard, so long 
as their shape does not depend on the diameter of the 
circles. Oblong protrusions of uniform width may 
press into any number of concentric circles without 
being affected by the increasing diameters. We are, in 



376 EXPOSITION AND ILLUSTRATION IN TEACHING 

fact, enabled to treat the oblong prolongations as mere 
lines. Ingenious people, of course, can introduce all 
manner of more or less useful complications/ 

It may very reasonably be questioned whether the 
general weakness that we have observed in estimating 
areas is an essential part of human nature. It may 
well be that this is merely a department of experience 
that has not received its proper share of attention. Ed- 
ucation has certainly done little towards training this 
particular mode of dealing with the materials presented 
by the outside world. Experiments have been made, it 
is true, but seldom on a large scale, or continued for a 
long time. Several years ago an enthusiast in educa- 
tion in the east of Scotland produced a scheme for the 
training of all our sense perceptions. On the analogy 
of Athletics, he called his system ^^Mentics.'^ It was 
not widely taken up, but in one or two cases it was 
applied with great thoroughness and success. An es- 
sential part of the scheme was a training in the estimat- 
ing of areas, and in one case, at least, in which it was 
applied the pupils developed quite a striking skill in 
estimating areas that happened to fall into the geo- 
metrical forms that had been used in their training. 
That is to say, the pupils could readily arrange in order 
of area a number of cardboard hexagons, triangles, 
squares, and other regular figures. They were less 
happy in arranging in order figures that had not occurred 
in their regular exercises, but they did much better 
work even with irregular figures than any class of 
equally intelligent but untrained pupils. On the 

^ For a very interesting example of this form of circular illustration, 
see the Report of the Minister of Public Instruction of New South 
Wales, 1908. (Physical Condition of Children.) 



THE DIAGRAM 377 

other hand, when the ^^mentically'^ trained pupils were 
taken into the country, they showed no unusual skill 
in estimating in acres the fields through which they 
passed; though looking at clearly marked fields from 
a height at some distance, they were able to compare 
with fair accuracy the areas of the different fields. 

There can be no doubt but that under the rapidly 
approaching development of handwork in all its 
branches in schools the area-sense will be much more 
highly cultivated than in the past, and even the bulk- 
sense will receive a certain amount of training. In the 
meantime, it is very difficult to get an ordinary pupil to 
understand how a fifty-cent microscope can be said, 
without actual lying, to magnify ^^ nearly 30,000 times,'' 
while a fifty-dollar instrument claims no more for 
itself than four or five hundred times, or seven hundred 
at the most. We may point out to the pupil that the 
first is estimated in cubical content and the second 
in diameters. But after we have explained that the 
cheaper microscope probably magnifies 30 diameters, 
or 900 {i.e, 30 x 30) area units, or 27,000 {i.e. 30 x 30 
X 30) cubic units, the pupil still finds a difficulty in 
taking in our meaning. To be fair to the good micro- 
scope, we must claim that it magnifies 343,000,000 times 
(700 X 700 X 700) . But this seems to prove too much. 
The pupil clearly thinks he is being imposed on. This 
enormous figure, he thinks, must be a mere ^^way of 
talking" — and he is right. As a matter of fact, ex- 
cept on the smallest scale, we cannot perceive cubical 
content ; we must deal with it as a matter of inference. 
We are all familiar with the very common confusion 
between eight feet square and eight square feet. But 
confusion is much more general when we deal with 



378 EXPOSITION AND ILLUSTRATION IN TEACHING 

cubic content. Most people who are preparing for 
their first ocean voyage make a very serious error in 
their interpretation of the 'Hwenty cubic feet/' or the 
''sixty cubic feet" allowed for baggage. Their minds 
are dazzled by a spaciousness in which an additional 
trunk or two are matters of no moment. Some people 
never acquire the volumetric sense, but have through- 
out life to take the shipping people's word for the 
surcharge. Others are amenable to the teachings of 
experience, and come to form a fair idea of what the 
phrase ''sixty cubic feet" means when expressed in 
crates and trunks. But while this form of inference 
may be trained, the process is a part of substantive 
teaching, and ought to precede the use of the area- or 
volumetric-sense as an aid in illustrating something 
else. Diagrammatic illustration offers a capital field 
for the sense when cultivated, but is not the field in 
which the cultivation should take place. 

Pending the further development of the area-sense, 
it will be wise to limit the range of the diagrammatic. 
Since the great value of the diagram is its abstractness, 
it does not seem desirable to carry it into a region 
where extraneous elements have to be taken into 
account. If we can represent all we want by means of 
straight lines, why should we seek for a more complicated 
medium ? When we know that Indiana is only one- 
hundredth part of the area of the whole of the states, 
why should we seek for illustrations that only' hamper 
our freedom in dealing with this fact? After all, it is a 
quantitative fact, and should not be confounded with a 
qualitative one. It is true that after we have mastered 
this mere numerical ratio, we have a very great deal to 
learn before we can apply this knowledge intelligently. 



THE DIAGRAM 379 

Mere area is not everything. But the necessary 
amplification of our knowledge is to be brought about 
by other forms of illustration. We shall understand 
the meaning of Indiana and the United States a little, 
but not much, better because we have learnt that a 
certain white circle is one hundred times as big as a 
certain black one. What is wanted after that is an 
application of the principle of elaboration. So far as 
mere quantity is concerned, we have enough when we 
have the bald statement of the ratio. 

One of the best illustrations of the application of the 
Jacototian principle, '^ Learn one thing thoroughly and 
refer everything else to it,'' is to be found in a diagram 
(figure 12) that occurred in the geography book ^ on 
which I exhausted my boyish enthusiasm. Unfortu- 
nately, my teacher did not attend to the Note at the 
foot. The diagram was always taken for granted, so 
that a large number of my classmates never quite 
knew what was meant by the remarks that headed the 
various countries dealt with in the text. For example, 
under Peru, one read ^^ Latitude in the middle the same 
as the south of Lower Guinea"; and under Arabia, 
^^Same latitude as from the middle of Morocco to the 
middle of Senegambia." In schools, however, where 
the book is properly used (for it has still a wide sale), 
there is continual reference to the diagram, with the 
result that the pupils learn to know exceedingly well 
the relative positions of the different countries on the 
face of the globe. Naturally, this is not the final stage 
in teaching relative position on the earth's surface. 
It represents the pictorial stage, or perhaps, better, the 
pictorial aspect. There is not only room, but necessity, 

^ Modern Geography for the Use of Schools, by Robert Anderson. 



380 EXPOSITION AND ILLUSTRATION IN TEACHING 




Note. — Teachers are requested to see that their pupils thoroughly master 
this brief lesson. The position of these eleven countries, which occupy the 

western shores of the Old Wojrld, is used to indicatcihe latitude of all. other 
countries of_the globe. 

Fig. 12.1 



* Reproduced by kind permission of Messrs. Thomas Nelson and 
Sons, London and New York. 



THE DIAGRAM 381 

for the freer indication of position on the surface of the 
globe as indicated by latitude and longitude. But the 
diagram follows the laws of good teaching in beginning 
with the matter and ending with the form. A similar 
diagram of the Eastern states might be used with very 
great advantage in teaching the relative positions of the 
various parts of the Union. When we are given the 
latitude and longitude of Georgia and Oregon, we can, by 
referring to a common standard reason out their rela- 
tive positions. But in facts that are so close to our 
everyday life it is well to get, wherever possible, at 
immediate connections. If we fni the position of a given 
state, by reference to a certain state on the Eastern 
coast, we are working up our complex of the states as a 
whole. 

Speaking generally, a diagrammatic illustration should 
be reduced to its lowest possible terms. Caran d'Ache, 
Phil May, and other artists who dazzle us by the fewness 
of their lines, seek quite a different effect from that 
proper to the diagram.^ Their aim is to reach the maxi- 
mum of suggestiveness with the minimum of representa- 
tion. They invite the spectator to supply as full details 
as he can, and their success is measured by the con- 
trast between the exiguous presentation and the ex- 

^ We are told that such artists make their first drawings in the 
ordinary way, filling in all the details so as to get a broad general eff"ect. 
Then they proceed to discover which lines are essential, and by a grad- 
ual process of elimination they reach the effective skeleton that is 
finally reproduced. The same thing is true of writing. Mr. H. G. 
Wells, for example, tells us that he first writes down things as they 
come into his mind, so as to "get some idea of the shape of" his 
subject. This first writing he calls "slush," and it is ruthlessly cut 
down as the book approaches completion. The "slush" may amount 
to over 100,000 words, the completed book to 55,000. (Interview 
in To-day, Sept. 11, 1897). 



382 EXPOSITION AND ILLUSTRATION IN TEACHING 

uberant mental picture. The diagram, on the other 
hand, seeks to confine the attention to one particular 
direction. It seeks to illustrate one relation. Caran 
d'Ache invites to an exercise in elaboration, the dia- 
gram to an exercise in elimination. A curious illustra- 
tion of this invitation to elaboration was supplied some 





189^ 
1890 

Fig. 13. 

years ago when there was a passing fashion in what was 
called ^'match-drawing.'^ This consisted in represent- 
ing human beings by means of straight lines only, as a 
child might do by placing matches on a table, so as to 
represent the trunk, legs, and arms. The interesting 
point for us is the skill with which the draughtsmen 
could suggest characteristic attitudes with this very 
limited means of expression. Fencers, boxers, walkers, 
runners, were all reproduced in the penny illustrated 
magazines in such a way that the spectator had to fill 
in the details whether he would or no. Sometimes 
match-drawing is used for real illustration. Thus, in 
a journal called Cycling, on July 22, 1894, there ap- 
peared the preceding drawing, figure 13, to illustrate the 
difference of the attitude in riding the bicycle in the 
year 1890 and in the year 1894. It appears that be- 



THE DIAGRAM 383 

tween these two dates a lamentable degeneration had 
taken place, owing to the scorching habit. It is to be 
hoped that the accompanying sketches represent an 
exaggeration: what we are certain of is that they viv- 
idly represent the views of the magazine writer. The 
reader's attention is not distracted by the personal 
appearance of the riders, or the qualities of the machines. 
Only the essentials appear. 

There is a certain amount of complication involved 
here, since suggestion will naturally invite to poten- 
tial elaboration. One may read as much anatomy and 
physiology and fashion into the figures as one's know- 
ledge admits. But there is not a line in the illustration 
that can be fairly called non-essential. We have here 
practically reached the limits of suggestion by resem- 
blance in a diagram. 

There remains that kind of diagram that represents 
certain truths without indicating any sort of resem- 
blance between the lines and forms used and the con- 
tent of the complex that forms the illustrandum. All 
the newer graphic methods used in the teaching of 
mathematics belong to this class, and all the various 
schemes of plotting out results in charts. The ac- 
companying diagram, figure 14, for example, has no re- 
semblance to either work or fatigue, yet it represents 
in a very efficient way the relation between fatigue 
effect and practice effect in determining the amount of 
intellectual work done in a given time. The abscissa, 
OM, represents the length of time the test lasted, in 
this case two hours. The ordinate, OL, represents 
the amount of work done. The work begins at A, and 
for a little time, through distraction and the effort to 
concentrate, there is a slight diminution of efficiency in 



384 EXPOSITION AND ILLUSTRATION IN TEACHING 

work. At B the practice effect begins to tell, and the 
line gradually rises to C. At this point the practice 
effect is counterbalanced by the fatigue effect that goes 




o length of time the test lasted: in this case two hours m 
Fig. 14.1 



on increasing, while the practice effect cannot increase 
further. The result is that there is a gradual falling off 
in the effectiveness of the work till we reach D. Here 
the prospect of a speedy release from effort, along with 
a quickening of the conscience, in view of the approach- 
ing end of further opportunity, gives a little fillip to the 
student, and his effectiveness rises somewhat till the 
two hours end at E.^ 

The value of such diagrams is that we can envisage at 
one glance a large number of facts that would baffle 
any mind to deal with when presented seriatim. 
What Professor Karl Pearson calls an ''observation 
frequency polygon," ^ and Mr. Graham Wallas (from a 

* Reproduced by kind permission of Messrs. Schleicher Fr^res, 
Paris. 

2 A. Binet and V. Henri : La Fatigue Intellectuelle, p. 239. 

^ For illustrations, see the periodical Biometrika, passim, or Karl 
Pearson's Chances of Death. 



THE DIAGRAM 385 

vague memory of its shape) calls a '^ cocked hat/' ^ is 
one of the best examples of this graphic aid to think- 
ing. Mr. Wallas quotes from Professor Marshall ^ in 
support of the statement that qualitative reasoning in 
economics is passing away and quantitative reasoning is 
beginning to take its place.^ Among my postgraduate 
(science) students, many of whom have studied under 
Professor Karl Pearson, and most of whom have been 
influenced by him, I note an increasing tendency to 
think in diagrams. I come across this line-thinking 
in all manner of unexpected places. An essay on the 
Shakespeare-Bacon controversy was full of ^^ cocked 
hats," and in an essay handed in the other day on the 
interactions between pupil and teacher, I found the 
whole positions set out in a sort of diagram of forces. 

The now common school plan of recording such 
matters as lengths of shadows, temperatures, baro- 
metric pressures, school attendances, have rendered 
the chart form of illustration familiar even to young 
children. It is true that these records are treated 
as processes of instruction rather than of illustration, 
and in the preparation of the curves there is training 
of a very valuable kind. Children are, in fact, being 
taught to think quantitatively. For our present pur- 
pose the important point is that pupils are now pre- 
pared by their substantive school work to understand 
all manner of chart illustrations. 

We have seen already the value of the straight line 



^ Human Nature in Politics, 1908, p. 133. 

2 Journal of Economics, March, 1907, pp. 7 and 8. 

3 Human Nature in Politics, p. 143. Here Mr. Wallas gives a very 
amusing and enlightening illustration of quantitative thinking on the 
subject of the best size for a debating hall of given shape. 

2c 



386 EXPOSITION AND ILLUSTRATION IN TEACHING 

as the best way of indicating a comparison in one single 
element, as area, or length, or cost, or weight. But 
there is another way in which the straight line has a 
special illustrative value. In dealing with mental 
activity we find that sense of direction is character- 
istic of mental functioning. ^^When this ^direction' is 
determined for me," says Dr. James Ward, '^I am said 
to be passive; when it is determined by me, I am said 
to be active.''^ There appears to be something more 
than mere metaphor in this psychological use of the 
word direction. Here is what Professor S. Alexander 
has to say on the subject: — 

"Now that I know what my brain is, I feel my thought occurring 
there, or, if not there, in some other part of my body. It is only 
as thus understood in connection with the bodily organism that I 
can say my mental activity is a movement with direction. But in 
this sense it is a movement that does occur in time and space. 
In other words, my mental activity is always qualified by what, on 
the analogy of local signs, I must call signs of direction.'' ^ 

Without laying too much stress on the psychological 
basis thus suggested, it may fairly be said that the 
straight line in certain diagrams performs the functions 
of those signs of direction. In a genealogical table the 
lines really do direct the mind, which in following this 
direction shows itself to be in this case passive. It is a 
matter of common experience that the mind is dominated 
by arrows and other indications of direction as they 
appear in graphic form. That such indications are a 
saving of thought effort is proved by their use in the 
graphic humour of the Sunday papers, in which it is 
now customary to indicate the direction of a projectile 

^ Proceedings of the Aristotelian Society, 1908, p. 226. 
2 Ihid., p. 220. 



THE DIAGRAM 387 

by dotted lines, so that the indolent spectator may be 
saved even the trifling trouble of discovering from which 
direction the projectile came on its fun-making errand. 
The plain man's desire ^Ho see a thing in black and 
white" is better met by a linear diagram than in any 
other way. Even when the letterpress is perfectly 

THE TEACHER'S USE OF LANGUAGE. 
THE BRIDGE 




( BUT 

J SOMETIMES 
J NOT 

V I 



FAMILIAR 

UNDEBSTOOO 



EXAMPLE. 



HAVE TW KINDS 
I. OF MEA NINGS 

EXAMPLBr ^*— *~->^ " 

DOG SUGGESTS X X /^ X DOoTl'irrFVs'Ta 

1. FOUR-LEGGEDNE83, / \ f \ i rftb?^vfJ 

■II HAIRINESS ) /cONNOTATIOnX / DENOTATION \ ( , " ^^YernaRO 

/^T^'i-^E^E^D^N^SS A QUALITIES J TH?n"gS { <" FOX-tSeR 

'Y:STEDNElf -^V J \ / V-P00DL°."'''^'° 

etc.; etc. \,__,^ \^____^/ ^- poodle 

Fig. 15. 

simple, the reader frequently likes to have a diagram- 
matic representation. In 1903 I published a little 
Primer on Teaching meant specially for Sunday-school 
people. Naturally I wished to make the text as simple 
as possible, and thought that I had made it so plain 
that no one could need any help to understand its 
meaning. Some time after its publication I received 
from a clever engineer ^ in New York a set of eleven 
diagrams that give a graphic representation of the 
main points in the various chapters. The engineer was 
the superintendent of a Sunday-school, and told me 

^ Mr. John Calder. 



388 EXPOSITION AND ILLUSTRATION IN TEACHING 

that he found his teachers understood the book in a 
much more practical way after he had given them his 
diagrams. Figure 15 reproduces one of these diagrams. 
On looking at it, one would think that the matter 
could have been equally well expressed in plain verbal 
exposition. But on putting the matter to several 
fairly well-educated Sunday-school teachers, I found 
that they, on the whole, preferred to have the diagram, 
but were good enough to admit that it must come after 
the text. 

We need be the less surprised, then, to find diagrams 
in such abstract books as Mr. W. MacdougalFs Social 
Psychology. In introducing an admirably clear exposi- 
tion of the neural bases of the sentiments of hate and 
love he says: ^^It is, I think, helpful, at least to those 
who make use of visual imagery, to attempt to picture 
a sentiment as a nervous disposition and to schematise 
it crudely by the aid of a diagram/' ^ As a matter of 
fact, the diagram consists of a row of seven small circles, 
each representing one of the primary emotional dis- 
positions. The rest consists merely of certain lines and 
arrows indicating direction. These lines have a com- 
pelling power, and cause the mind to follow them al- 
most in spite of itself. They are more useful in help- 
ing the student to understand than in helping him to 
recall details. 

It has to be noted that the mere presence of the lines 
helps to fix the attention. This is the justification 
of the habit some capable teachers have of making 
what seem quite unnecessary lines on the blackboard. 
They will put down this sort of thing on the blackboard 
and accompany it by something like the following: 

^ Social Psychology, p. 124. 



THE DIAGRAM 



389 



''Let A represent Walpole, B Queen Caroline, and C 
George the Third. The natural way of communicat- 
ing with the king would have been for the minister to 
speak directly to him; but as a matter of fact, impor- 
tant communications usually took the route indicated 
by the arrows.^' All that this triangular method im- 

A 

B 



plies has, of course, to be brought out by the teacher, 
but he feels that he has had a greater grip on the pupil's 
attention because of the apparently unnecessary figure. 
When I suggested to the teacher that it might have been 
better to use significant letters, W, C, and G, he main- 
tained — influenced, no doubt, by his memories of math- 
ematics — that the 
more conventional the 
symbols the better. 
To put the actual 
names Walpole, Caro- 
line, and George would, 
he maintained, have 
spoiled everything. 
Here he differed from 
the originator^ of this 
illustration — strangely 
enough the teacher to whom I spoke seemed to re- 
gard the illustration as his own — who uses the signi- 
ficant initials W, K, and Q. The view that significant 
letters are objectionable is evidently adopted by the 
writers of the Public School Latin Primer, in which the 

*R. Somervell in P. A. Barnett's Teaching and Organisation, p. 171. 




Fig. 16. 



390 EXPOSITION AND ILLUSTRATION IN TEACHING 

solitary little diagram in the book, figure 16, illustrates 
case by means of letters without significance : — 

— " Case {casus, from cado) is, literally, a falling. Grammarians rep- 
resented that form which a Noun takes when it is the Subject of a 
sentence by an upright line, as AB, and likened the other forms to 
lines falling away from the perpendicular at various angles, as, AC, 
AD, AE, AF, etc. These they called Cases; and their series, the 
declension, declining, or sloping down of the word. Afterwards, 
the Nominative or Subject case was called (with evident impropriety) 
Casus Rectus, the Upright Case, and the others (except the Voca- 
tive), Casus Obliqui, Oblique Cases; whereas the Stem {or Crude form) 
of the word is more properly the upright Hne, and the several cases, 
including the Nominative and Vocative, are branches deflecting 
from it. So, from the Stem nuc- (walnut-tree), the Cases are : N. V., 
nuc-s (-ux). Ace, nuc-em, G., nuc-is, D., nuc-i, Ab., nuc-e.'' ^ 

Probably the influence of custom on the schoolmaster 
in making ^'Diagrams of Illustration'^ in Euclid had a 
good deal to do with the selection in this case of the 
first letters of the alphabet. At any rate, in actual 
exposition to a class, experience shows that it is better 
to adopt significant letters. is substituted for A, and 
S for B; thus, OS represents the stem; then Ace. would 
represent the accusative, OG the genitive, and so on. 
It would seem that the pupil can hardly understand the 
meaning of case much better from seeing his teacher 
draw seven lines from a given point; but in practice it 
is said that the drawing does actually help. Probably 
some, at least, of the advantage comes from the draining 
off of a certain amount of nervous energy on the part 
of both teacher and pupil, an energy that might other- 
wise interfere with the learning process, just as in think- 
ing out riders in Euclid the pupil works more steadily 
when he has a pencil in his hand, even if he makes no 
use of it in the way of either drawing or writing. 

' P. 154. 



CHAPTER XVI 

Dangers of Illustration 

As an ending to a question the words '^Give exam- 
ples/' are very dear to the heart of the examiner. 
With those who are called upon to write answers to ex- 
amination questions, the words are not quite so popular. 
The complaint of the examiners is that the examples 
given are stereotyped. If an example is given in a 
text-book, it reappears with cloying persistency in the 
answers. Out of nine hundred answers to a question 
in a Board of Education school management paper 
asking for an example of one word being run into an- 
other in reading aloud, over six hundred gave ^Hhis 
shrub" the actual phrase used in a then popular text- 
book. Very few candidates had the originality even to 
change the letters while retaining the actual example, 
as in ^Hhis stable." 

Experience shows that there is a strong tendency to 
fall into ruts in illustrating any particular point. Ask 
a class for examples of sentences. If the first pupil 
says ^^Cows eat grass," the chances are that his fel- 
lows will go on mentioning what other animals eat. If 
we wish to provide reasonably varied examples for 
class work, we must consider beforehand which illus- 
trations we shall use in a given lesson. It is the com- 
monest thing in the world to find a teacher depending 
for his illustrations on the spur of the moment. If he 

391 



392 EXPOSITION AND ILLUSTRATION IN TEACHING 

has a mind particularly well stored with matter on the 
subject he is dealing with, he may escape from the seri- 
ous defect of supplying tiresome strings of more or less 
similar and eminently commonplace examples of the 
rules he is expounding. It is easy enough to supply 
almost unlimited quantities of examples of particular 
kinds of nouns and verbs, or of natural orders in botany, 
or of islands in geography. In writing on the black- 
board sums to be worked out, the teacher finds that the 
numbers come without the least difficulty. In all these 
cases the connection between the rule and the example 
is so clear that no mistake is possible except through 
such culpable ignorance as is seldom to be found among 
teachers. Here one example does almost as well as 
another. The content of the individual example does 
not affect the general rule to be illustrated. 

So far, what may be called the hand-to-mouth method 
of illustration is innocuous, and is even advantageous, 
since it saves unnecessary labour. So soon as the con- 
tent of the illustration becomes of importance, the 
method will be found to be full of danger. The teacher 
who carelessly dictates at random half a dozen English 
sentences to be translated into Latin to illustrate the 
construction of cum with the subjunctive, may lead to 
all manner of confusion among his pupils, because they 
find in the sentences other difficulties than those con- 
nected with cunij difficulties that have not been pre- 
pared for by any previous instruction. A teacher's 
brilliant scholarship is no safeguard against error here. 
All such illustrative sentences must be carefully edited 
by the teacher in the light of what he knows of the previ- 
ous training of his pupils. No doubt there comes at a 
later stage of instruction in Latin prose a time when the 



DANGERS OF ILLUSTRATION 393 

pupils must be prepared to deal with unedited English 
passages for translation into Latin; for at that stage 
they have a sufficiently wide knowledge of Latin con- 
struction to allow them to exercise a certain freedom. 
But even at this stage the master must not select his 
English passage entirely at random. Certain passages 
cannot be translated into Latin, since they contain 
words and ideas that the classical writers have not 
had the forethought to anticipate. 

Some teachers escape the dangers of the hand-to- 
mouth illustration by more or less unconsciously ac- 
quiring a stock of illustrations that they stereotype, 
and keep in hand so as to produce them on appropriate 
occasions. Great weariness often results for the pupils 
who have to submit to the same illustration without 
explanatory comments that might make it intelligible. 
As soon as the question of transitive or intransitive 
came up, a certain teacher might be relied upon to 
make the following remark, and no other: ^^The cat 
cannot sit the mat, therefore sit is intransitive. '^ Years 
afterwards that teacher's pupils spoke with bitterness 
of that intransitive cat. The reproach of the stereo- 
typed illustration is removed when it can be shown that 
it is a real touchstone of truth that may be applied to all 
cases within its sphere. For instance, there is a peren- 
nial difficulty among young students of French about 
which of the verbs take etre and which avoir in conju- 
gating their past tenses. Some text-books deliberately 
give lists of verbs that are conjugated with avoir, and 
no attempt is made to lay down the principle that may 
explain this peculiarity. This principle seems to be 
that where the action of the verb is followed by a corre- 
sponding state, the verb Ure is to be used ; in all other 



394 EXPOSITION AND ILLUSTRATION IN TEACHING 

cases, the verb avoir. The stereotyped test is in the 
form of the question : ^' If the subject has done so-and-so, 
is it so-and-so?'^ This is obviously obscure, so a parti- 
cular case is taken. ^'If the subject has come, is it 
comef^^ If the answer is yes, then etre is the verb; 
if no, then avoir. It may be simpler to adopt the form 
of the second person: '^If you have done so-and-so, are 
you so-and-so?'^ ^'If you have eaten, are you eaten?'' 
No; then use avoir. But whatever the form, it must 
enable us to discriminate between those cases in which 
a verb sometimes has etre and sometimes avoir. Take 
the verb descendre, with the subject le chef. '^If le chef 
has descended, is he descended?" Yes; therefore etre. 
"If le chef has descended the dinner, is he descended?" 
No ; therefore avoir. Le chef a descendu le diner. 

So with the simpler case of quotation marks in writ- 
ing a dialogue. The pupil may be given the stereo- 
typed question: Did the speaker open his mouth and 
let out the very words in question? If the answer is 
yes, then quotation marks must be used. With duller 
pupils some teachers adopt the grosser device of making 
the pupils ask themselves whether the doubtful words 
could be represented within the bladders of words that 
are drawn as coming out of the mouths of persons in in- 
ferior comic cartoons. The method may be objection- 
able because of its associations with trashy literature, 
but so far as being stereotyped is concerned, no harm is 
done, since the illustration is of universal application. 

In almost every subject the hand-to-mouth illustra- 
tor gets into trouble by demanding from his pupils 
knowledge that is not yet due in the course of their 
study. It is probably unnecessary to labour this 
point here, for the reader who has taken the trouble to 



DANGERS OF ILLUSTRATION 395 

follow this book so far has given proof that he has 
enough interest in the subject of method to prevent his 
making the discreditable bungles that not infrequently 
mark the teaching of brilliant scholars who rely upon 
their mere knowledge of the subject to carry them 
through, without taking the trouble necessary to make 
their teaching efficient. The reader^s danger may in- 
deed be quite the opposite. Because of his interest in 
the theoretical aspect of his work, he may be inclined to 
over-elaborate his illustrations, and may thus fall into 
certain errors that are likely to interfere with the suc- 
cess of his teaching. 

To begin with, there is the danger of over-illustration. 
Some teachers seem to regard it as an established prin- 
ciple that every point that arises must be illustrated, 
whether it offer any difficulty or not. What is per- 
fectly clear already needs no illustration as a matter of 
Exposition. A straightforward statement of fact deal- 
ing with elements that come well within the pupiFs 
range should not be illustrated, so long as the teacher's 
purpose at the time is only to get the pupil to under- 
stand. Indeed, it is possible that by illustrating what 
requires no illustration the teacher may cause needless 
difficulty to arise, especially in the minds of the more 
eager and attentive pupils. Accustomed to attach 
a meaning to all the teacher says, such pupils are apt 
to think that since he makes so much of the point he 
is labouring, there must be something in it which they 
do not yet perceive, and they may grope about for a 
meaning that is not there. 

By the commonplace teacher the temptation to over- 
illustration is easily resisted. His danger lies in quite a 
different direction. But there is a very real risk in the 



396 EXPOSITION AND ILLUSTRATION IN TEACHING 

case of the zealous expositor. No limit can be set to the 
possibilities of illustration, once the lust of the collector 
is joined to the enthusiasm of the teacher. Every keen 
expositor is a potential grangerite. 

"In our time the term 'grangerite ' has come to be applied to 
the commentator who summons illustration to his aid in dealing 
with a book already printed. That, however, does not cover his 
art, which includes everything bearing on the elucidation of the text. 
I use the word 'grangerising,' then, as a term for the general art of 
what may be called the methodised scrap-book — for in its very 
method it differs widely from the oUa-podrida usually known by 
that name." ^ 

The art, named after the Rev. James Granger, who 
began life in Dorset, England, in 1723, is full of attrac- 
tion, not to say temptation, for the industrious and in- 
genious teacher. When he is taking a class through one 
of Shakespeare's plays, and as a help in his preparation 
cuts up two cheap copies of the text and pastes the sepa- 
rate leaves each in the middle of one of the pages of a 
large manuscript book, so that he may fill the abundant 
margin thus supplied with notes of all kinds on the text, 
he may not know that he has set out on a grangerising 
expedition. He cuts out some critical remarks from 
newspapers or magazines and pastes them in his book. 
If he can get pictures, he naturally includes them in his 
collection. By and by it is clear that even the huge 
manuscript page is insufficient, and a new book is neces- 
sary. He is not likely to go to the excess that drove 
Lefevre to grangerise Voltaire into ninety volumes, 
but he may very easily be carried away beyond the 
bounds of prudence. Kept within modest hmits, a 
grangerised copy of a classic to be studied or a text- 

1 J. M. Bullock : The Art of Extra- Illustration (1903) p. 10. 



DANGERS OF ILLUSTRATION 397 

book to be taught is a valuable possession, both for the 
information it actually contains and for the mastery of 
the subject that its compilation helps to secure. But 
there is always the danger of the collecting interest 
getting the upper hand, and the book becoming an 
end in itself. Instead of illustrating the original text, 
it dwarfs that text, swamps it, drowns it. The teacher 
must never forget that as teacher his interest lies in ex- 
pounding the text or other subject. His illustrations 
are to be illustrations of the original subject. The 
grangeriser very rapidly gets off the main line and goes 
on illustrating illustrations, till the real subject is left 
far behind. What the teacher must avoid is well 
exemplified in Hill Burton's caricature of the granger- 
ite's methods of illustrating the familiar lines: — 

How doth the little busy bee 

Improve each shining hour, 
And gather honey all the day 

From every opening flower. 

"He pictured him starting with the poet, Isaac Watts. This 
would suggest all manner of bees, — Attic and other, — and all sorts of 
beehives would be appropriate, to be followed by portraits of Huber 
and other bee-collectors, and views of Mount Hybla and other 
honey districts. Burton poured good-humoured contempt on the 
process by drawing out the agony of subjects to be illustrated; 
but in the forty years that have elapsed since he penned the Book 
Hunter, the subject of the bee has been extended to a point more 
elaborate than Burton ever contemplated. To-day the exhaustive 
(and exhausting) grangerite would have to include, for example, 
a portrait of Maeterlinck, who has told us the story of the bee in 
terms of the most charming philosophy, to say nothing of Lord 
Avebury's many works, and the scientific construction of the bee- 
hive. Burton then went on to say that the grangerite would have 
to remember that there was once a periodical called the Bee, edited 
by Dr. Anderson, who was the grandfather of Sir James Outram, 



398 EXPOSITION AND ILLUSTRATION IN TEACHING 

whose career might be included. Finally, he genially suggested 
that, when the illustrator came to the last hne, * which invites him to 
add to what he has already collected a representative of every 
opening flower, it is easy indeed to see that he had a rich garden of 
delights before him. '" ^ 

A French psychologist, writing on the theory of 
laughter, admits that he used to read the examples of 
fallacious reasoning in his text-book on logic, as a sort of 
legitimate jest-book. George Eliot gives us a delight- 
fully true account of the seductive charms of the 
matter supplied in the illustrative examples in the 
Latin grammar. Maggie TuUiver : — 

"presently made up her mind to skip the rules in the Syntax — 
the examples became so absorbing. These mysterious sentences 
snatched from an unknown context — like strange horns of beasts, 
and leaves of unknown plants, brought from some far-off region — 
gave boundless scope for her imagination — the fortunate gentle- 
man whom every one congratulated because he had a son 'en- 
dowed with such a disposition ' afforded her a great deal of pleasant 
conjecture; and she was quite lost in the 'thick grove penetrable 
by no star.'"'' 

We have here a force with which every teacher has 
to reckon, the examples always have been and always 
will be so absorbing. As a rule they are not in them- 
selves dangerously interesting: they usually obtain 
their power by contrast with the still less entertaining 
matter of the text. Even the pubhsher's advertise- 
ments at the end of the book are not without their 
attractions as a relief from what the book itself con- 
tains. Making all allowance for this unearned incre- 
ment of interest that attaches to examples, we find that 

1 J. M. Bullock; T/ie Art of Extra Illustration, p. 19 (published 1903). 
The original passage will be found in The Book Hunter, Part I, "Class- 
ification." 2 ]\j;j^ii Q^ if^Q Floss, Book II, Chap. I. 



DANGERS OF ILLUSTRATION 399 

the legitimate attraction of the examples is a dangerous 
rival to the teacher. The way to meet the difficulty is 
not to make all the examples of the most uninteresting 
character, but to select them, as far as possible, from 
matter that has already exhausted its interest in 
other parts of school work. Let the teacher consider 
the wiles of the clever advertising tailor and learn of him. 
In a certain shop in Holborn, London, there appeared 
a little while ago a new set of wax heads to surmount the 
dummies that displayed the ready-made suits in the 
window. The new heads were exceedingly well made 
and formed a very agreeable change from the wooden 
knobs that had formerly finished off the dummies. 
The passers-by were greatly interested, and gave un- 
stinted admiration to the type of head adopted. There 
was, however, one fatal defect from the point of view 
of the critical public. The whole thirteen heads were 
of exactly the same pattern; in fact, they were the same 
head, cast in the same mould, coloured with the same 
pigments and by the same process, supplied with the 
same glass eyes and the same curly brown hair. On 
being remonstrated with, the tailor admitted that his 
aim was not entirely disinterested. The heads were 
specially good in order to attract attention to his 
window. They were made exactly alike so as to ex- 
haust very rapidly the interest of the onlooker, who, 
disappointed at the similarity, sought for and obtained 
the necessary variety by examining the different kinds 
of suits of clothes. 

In the case of teachers who use as examples matter 
that has already exhausted its interest in other depart- 
ments of school work, there is a double end served — 
old matter is revised, and a new interest is created in it, 



400 EXPOSITION AND ILLUSTRATION IN TEACHING 

which new interest is of exactly the kind the teacher 
desires to arouse, for it is connected with the work 
actually in hand. The pupil is interested to know what 
the teacher is going to do with this familiar old fact 
that is being presented. The whole question of corre- 
lation is involved here. Teachers are now aware of the 
dangers of weariness that are implicit in the overzeal- 
ous use of correlation. But our present consideration 
recognises the loss of interest in certain parts 9f school 
work, and proposes to take advantage of this loss. 
Certain matter is selected because it has lost its in- 
trinsic interest, and if, in the process of teaching, a cer- 
tain amount of mediate interest is developed, that is 
all to the good. 

One of the chief dangers of the use of illustration is 
connected with this problem of the incidence of atten- 
tion. There is always the risk that the illustration 
will prove more attractive than the illustrandum. 
The attraction to which Maggie Tulliver yielded is not 
confined to examples. An illustration fails when it 
derails the interest of the pupils from the main lines of 
the lesson. In the case of certain material illustrations, 
such as models or pictures, the derailing of interest is so 
obvious that it at once attracts the teacher's attention, 
and he takes means to recall it to the main subject. 
This is comparatively easily done if he has the sense to 
allow the illustration to exhaust most of its primitive 
interest before he proceeds to use it as a mere illustra- 
tion. It used to be a matter of professional pride with 
a class teacher not to let a particularly interesting ob- 
ject be seen till the moment came at which it had to be 
produced for illustration. No great harm resulted if, 
when it was introduced, the teacher allowed a reason- 



DANGERS OF ILLUSTRATION 401 

able time for the pupils to gloat over it before he began 
to demand their attention to its purely illustrative 
aspect. The skilful lecturer, on presenting an attrac- 
tive slide on the screen, follows the plan recommended 
in Chapter VIII,^ and allows a reasonable time for the 
subsidence of that gasp of appreciation with its suc- 
ceeding murmur of whispers that welcomes every strik- 
ing picture. When he does begin to talk, he takes care 
to deal with comparatively unimportant matters till 
the edge of the intrinsic interest of the slide is blunted. 
If the slide is really important as an illustration, he 
may introduce it at an early stage in his lecture mainly 
to rub off its intrinsic attraction. At its first appear- 
ance he merely calls attention to facts that are in any 
case attracting the attention of his audience; when, 
at a later stage, it reappears, he is able to direct the 
attention of his hearers in the way he desires, for they 
are now able to concentrate on the line of secondary 
interest as brought out in the illustrative process. 

Too frequently the derailing of interest is not antici- 
pated by the teacher, because he has failed to consider 
the immediately preceding content of the minds of the 
pupils. Any reference to certain of the more urgent 
interests of the pupils may be an excellent way of getting 
up a secondary interest in some part of school work. 
Mensuration may be connected with the football field 
or the cricket pitch, hydrostatics with boating, dynam- 
ics with the proceedings in the gymnasium. But in 
all such cases there is great danger of derailing the in- 
terest from the school subject. No doubt it may be 
won back again, but in a case of class instruction it is 
probable that the temporary aberration has caused at 

'p. 208. 
2d 



402 EXPOSITION AND ILLUSTRATION IN TEACHING 

least a few pupils to lose some important link that they 
may not be able to catch up during the course of the 
lesson. 

The teacher has to remember that every illustration 
he uses must run the gantlet of divergent association in 
the mind of every one in his class. He can never be 
quite sure that the most innocent illustration may not 
derail the interest of some of his pupils, even though 
he takes all possible precautions. But he ought at least 
to minimise the danger by doing all he can to remove 
temptations. For example, he must avoid the arith- 
metical challenge^ of which we have already had one or 
two examples.^ Certain minds are so constituted that 
as soon as two terms of an arithmetical problem are 
presented, they must proceed at once to work it out. 
If at one part of a literature lesson the master mentions 
that he first read Lycidas at the age of twelve, and at a 
later stage that it is now a quarter of a century since 
he first read Lycidas, sl large number of his pupils will 
neglect the point he is making in speaking of the differ- 
ent effect of Lycidas on the boy and on the man : their 
attention will be taken up in calculating the exact age 
of the master. Young people are particularly open to 
the arithmetical challenge when it implies a certain 
amount of criticism of a statement made. Though it 
was an adult mathematician who made the following 
arithmetical criticism of Tennyson, it is quite in the 
schoolboy vein. In his Vision of Sin Tennyson ven- 
tures the statement : — 

^ Pages 250, 309. An excellent example of the irritating effect of 
the challenge is to be found in the quotation from Mauclair on p. 337. 
The hourly change and the " twenty times " call for explanatory com- 
ment. 



DANGERS OF ILLUSTRATION 403 

"Every moment dies a man, 
Every moment one is born." 

The man of figures at once accepted the challenge, and 
pointed out that if this were true, the population of the 
world would necessarily remain stationary, which, of 
course, was contrary to recognised facts. He suggested 
as an emendation the following: — 

"Every moment dies a man, 
And one and a sixteenth is born." * 

He admitted that it was not absolutely accurate, but it 
was at least approximately correct. It is because this 
perverse mathematician takes such an unreasonable 
view that the story forms a useful illustration. The 
pupil ought to be thinking in terms of poetry; if he 
persists in thinking in terms of number, there is serious 
damage done to the lesson. Even when no reference to 
number is involved in the exposition, certain minds are 
tempted to introduce calculation. One of the students 
of an exceptionally slow lecturer at Oxford confessed 
that, in the inordinate pauses during the lecture, he ac- 
quired a habit of calculating what each pause cost him 
on the basis of so much for a course of twelve lectures 
of one hour each. The moral for the teacher is that 
Satan's employment bureau does not limit itself to 
manual labor. 

Teachers should be very careful in their use of the 
allusive style. Any reference, for example, to a person 
or place without mentioning the name will often set up a 
disturbance that takes quite a long time to settle down. 
To refer to Milton in a lesson merely as '^the author of 
the Defensio Populi AnglicanV^ may give satisfaction 

^ Quoted by Paratus in the British Weekly, June 3, 1909. 



404 EXPOSITION AND ILLUSTRATION IN TEACHING 

to a certain number of pupils who happen to know who 
is meant. But to certain others the reference will prove 
a stumbling-block, for they will go on wondering who it 
can be, when they should be following the work of the 
class. In this particular case the average boy would 
probably not trouble much, for the reference is not in 
itself interesting to him. But let the teacher use some 
superlative descriptive reference, and dissipation of 
attention will necessarily follow. ^'The worst king 
who ever ruled England,^' ^Hhe author of the longest 
poem in the English language,'^ are references that will 
disturb any intelligent class. It goes without saying 
that it is a laudable thing to be interested in discover- 
ing the actual persons referred to in such statements. 
The trouble is that the interest is roused at the wrong 
time. We are so fond of rousing interest that we are 
apt to forget that it is as necessary to allay interest 
as to excite it. In order that the interest of the pupils 
in the main subject of the lesson may be maintained, 
all subordinate interests must be ruthlessly dissipated. 
The way to kill an interest is to satisfy it. Nothing 
must be left for the imagination to work upon. Every- 
thing must be represented with pikestaff directness, 
and the mind will seek interest elsewhere. 

While writing the above paragraph I have furnished 
for myself an unexpected and involuntary illustration 
of my theme. No sooner had I written the words, 
'Hhe author of the longest poem in the English language,^' 
than I began to feel uncomfortable. I realised that I 
did not know who he was, and I began to wonder who 
he could possibly be. Milton wandered through my 
mind, and distracted my attention from the main sub- 
ject of the paragraph. I had an uneasy feeling that, 



DANGERS OF ILLUSTRATION 405 

though the Paradise Lost was long, it was far from being 
the longest poem in the English language. I had a 
vague memory of having heard the phrase ^Hhe longest 
poem in the English language'^ applied to Drayton's 
Polyolbion. But there came to me the disquieting im- 
pression that I had somewhere read that one of the in- 
dustrious early settlers in New England had outstripped 
Drayton. Could it be Michael Wigglesworth? Next I 
comforted myself with the reflection that all I had to do 
was to turn to some standard book on the subject of lit- 
erature, and get the matter settled; so I was able to dis- 
miss temporarily the troublesome interest in favour of 
the general interest, which was, in any case, the stronger. 
Had I been a careless pupil in a class with a sporting 
interest in superlatives, and little interest in what was 
going on at the time, it is probable that I should have 
continued to worry about that longest poem instead of 
turning to the main subject.^ 

As a test of the truth of the view here adopted, let the 
reader try to remember whether his attention was not a 
little dissipated, and if, indeed, he was not somewhat 
annoyed by the unfinished sentence, ''The most op- 
timistic writer on Education is . . .,'' introduced^ in 
Chapter I to illustrate the mind's tendency to anticipate 
what is coming. Since the hiatus has served its pur- 
pose, the reader is now entitled to the tardy explana- 

^ On referring to text-books, I found no help in settling the question, 
so I fell back upon an examination of some of the poems that might 
claim first rank. Paradise Lost reaches the modest total of a trifle 
over 10,500 lines. The Polyolbion attains to nearly 16,000. The 
Ring and the Book swells out to 21,133 lines. But the limit seems 
to be reached in Festus, a Poem, by Philip James Bailey, which, in 
its reorganised form (Fiftieth Anniversary Edition, 1893), reaches a 
total that on a rough calculation amounts to 40,800 lines. 

2 See p. 15. 



406 EXPOSITION AND ILLUSTRATION IN TEACHING 

tion that the writer referred to is Helvetius, who boldly 
proclaims " L'education peut tout/' 

Under certain conditions the allusive style may be 
excellent in print, but when used in lecturing or teaching, 
it ought to be limited to the most obvious allusions, 
allusions that are well within the range of the less 
informed of the class or audience, so that the main 
effect of the allusion will be to rouse that feeling of sat- 
isfaction that accompanies the recognition of an old 
friend under new circumstances. A typical example 
of the sort of thing that may perhaps be permitted in a 
book, but that must be excluded from oral teaching, is 
to be found in the extract from Madame de Coulevain 
in Chapter XI of this book/ There we find allusions to 
"si king," and to ^Hwo of our great newspapers, one of 
our best reviews." At this point Madame de Coule- 
vain' s reader puts his finger between the leaves and 
leans back, wondering who that king and what those 
publications can be. Unless from the point of view 
of piquancy, the allusions are a mistake in exposition. 
If there were any indication of how the missing names 
could be discovered by the reader for himself, there 
might be some justification for the mystification, since 
it would rouse him to take a fair share of the work. 
But as they stand, they only aggravate the reader by 
making him feel his ignorance and — it is no extenu- 
ating circumstance to add — Madame de Coulevain's 
superiority. Apart from this unprofitable disturbance 
of mind, the same end could be obtained by saying 
merely that a king could be as bourgeois as the tenant 
of a flat, and that some of our great newspapers and 
reviews are bourgeois. In a lecture or lesson the hearer 

1 See p. 294. 



DANGERS OF ILLUSTRATION 407 

would not only be irritated by the unintelligible allu- 
sion, he would, necessarily, from the distraction of his 
attention, lose a great deal of what immediately fol- 
lows the derailing references. If the authoress means 
Louis Philippe, why not say so? The names of the two 
great newspapers and the review would be much more 
illuminating than the piquant riddle she has set us. 
No doubt, in thus making our references specific we 
kill a certain amount of interest, but the interest killed 
is of the unhealthy, distracting kind; audit has always 
to be remembered that we are mainly concerned here 
with the didactic use of illustration. 

An author may feel that it is worth while to aggravate 
his duller readers so long as he wins the admiration of 
the clever, and if he is prepared to pay the price, there 
is nothing more to be said. The irritated reader, on his 
part, is free to throw aside the tantalising book. But 
when it comes to oral exposition, it is necessary to carry 
the whole of one^s audience with one. We cannot, of 
course, as Dr. Johnson pointed out with some asperity, 
supply our hearers with understanding, but we are not 
justified in distracting what understanding they pos- 
sess by leading it into blind alleys. 

I have had occasion already to refer to the teacher^s 
overgrown respect for accuracy. In certain forms of 
illustration this respect leads him into serious difficulties, 
for there practically emerge two kinds of accuracy, 
and these two kinds cannot be reconciled. He has to 
make a drawing of the earth as an ^^ oblate spheroid.'^ 
If he makes an accurate drawing, the pupils will be un- 
able to notice any difference between his drawing and an 
ordinary circle, but if he flattens the polar ends suffi- 
ciently to make the true shape apparent, he has played 



408 EXPOSITION AND ILLUSTRATION IN TEACHING 

havoc with the other kind of accuracy, and multiphed 
many times the paltry six-and-twenty miles by which 
the equatorial diameter exceeds the polar. Sir John 
Herschel may speak bluntly about circles representing 
the orbits of the planets, but knowing that the orbits are 
really ellipses, the teacher is in a strait between two. If 
he draws them as circles, he is inaccurate qualitatively, 
for they are not circles; but if he draws them elliptical 
enough to make his class easily perceive that they are 
not circles, then he has to err quantitatively. For they 
are not so elliptical as all that. Clearly, the teacher 
must be allowed sufficient quantitative exaggeration 
to make clear his qualitative distinctions. If his pupils 
are at a stage at which it is important that they should 
know that the earth is an oblate spheroid, then he must 
be permitted so to represent it as to suggest that particu- 
lar form. It is quite a different matter when little 
children are sedulously taught that the earth is '^nearly, 
but not quite, a perfect globe. '^ This is the same lust 
for accuracy that has canonised the additional two feet 
in the height of Kinchin junga — ^Hwenty-nine thou- 
sand and two feet.'' Naturally, inteUigent pupils will 
be warned when necessary exaggerations are made. 
They will be told, for example, that though the earth's 
orbit is elliptical, its major axis is not quite so big in 
proportion to the minor as the drawing would make out. 
Another very real danger in the use of illustration is the 
tendency to carry over the illustration as a whole with 
non-essential as well as essential elements. A teacher 
wished his class to understand that for a particular ex- 
periment he was describing it was necessary to cut out 
an oblong piece from the middle of one end of a board. 
As some of the pupils had a difficulty in understanding 



DANGERS OF ILLUSTRATION 409 

what he meant, he explained that the bit cut out was to 
leave a hole in the bottom of the board, so that when it 
was placed on end there would be an opening in it like 
the entrance to a dog's kennel. This seemed to satisfy 
the pupils, but at a later stage, when they had to make 
a drawing of the apparatus, several of them made the 
board appear as a pentagon, like the gable end of a 
house. They had carried the kennel comparison too 
far. What in this case could be tested by the sketches, 
would, in the case of merely verbal description, probably 
have escaped detection, and with young children, in 
particular, it is probable that many of our illustrations 
are carried over bodily and incorporated in connections 
in which certain of their elements are quite out of place.^ 
The teacher must be continually on his guard, and must 
try to anticipate and avoid possible misconceptions of 
this kind. Nearly always he will find that, in spite of 
all his endeavours, some dull, commonplace child has 
contrived an impossible combination that, had it been 
deliberately made, would be regarded as very ingenious. 
To meet such contingencies a certain amount of verbal 
pruning is necessary, but above all there ought to be a 
good deal of intercourse in the way of applying illustra- 
tions. A teacher in a city school, in giving a lesson on 
the Charge of the Light Brigade at Balaclava, made 
a sketch-plan on the blackboard, with the Russian guns 
on the right of the board and the formation of hussars 
represented by two vertical hnes on the left. The class 
as a whole seemed to understand the state of affairs on 
the field, but in the course of discussion it came out 
that some of the boys (the average age of the class was 
12+) thought a mistake had been made in the position 

^ Cf, the Castle misunderstanding, p. 112. 



410 EXPOSITION AND ILLUSTRATION IN TEACHING 

of the hussars. As they were represented, the boys 
maintained, they were charging either north or south 
instead of eastwards, as they ought to do if they meant 
to get at the Russian guns. On probing, the teacher 
discovered that the double line had misled the boys. 




There was a cavalry barracks in the city, and when the 
troops passed through the streets, they always went two 
abreast because of the traffic. The boys had got it into 
their heads that this two-abreast mode of progression 
was the natural one for cavalry, and that therefore they 
would charge in this order. It was a revelation to them 
that the charge was made with such a wide front. 

Allied to this error of carrying over non-essentials is 
that of arousing altogether wrong masses of ideas through 
some superficial resemblance. Beginners in landscape 
painting are warned against the little cottage on the 
hillside with its two tiny windows, one on each side of the 



DANGERS OF ILLUSTRATION 411 

door, and the little doorstep, with the resulting resem- 
blance to a grotesque human face. Not infrequently 
young people see a ludicrous aspect of some matter that 
to the adult mind appears to be of the most matter-of- 
fact character. ^' Speaking of babies," said the Sunday- 
school superintendent, ^^I have a baby in my eye now." 
He was quite serious, and did not at first understand 
what the youngsters found to laugh at in what he re- 
garded as a very commonplace statement. Occasion- 
ally private jokes of this kind interrupt the attention 
of individual pupils, but it is the business of a good 
teacher to anticipate and provide against any such 
misapplication of ordinary words, so far as such mis- 
applications are likely to affect a whole class. The 
teacher^s safety here depends upon his knowledge of 
the pupil's mental content. Unintentional jokes in 
class are always the mark either of ignorance or of bad 
psychology. 

Illustrations are often put in what the illustrator 
regards as a striking way, and yet are apt to mislead the 
pupils because of their very vividness. I have heard a 
teacher, in seeking to give his class an adequate idea of the 
size of London, make the statement that if all the houses 
in that city were placed end to end, they would reach 
right round the earth, following the equator. In dealing 
with the class afterwards, I found that the general 
impression produced was complicated by an incongru- 
ous picture in the pupils' minds of an interminable 
street, with only one side to it. Quite a number of the 
pupils had the literal objection that most of the houses 
would be flooded, as the equator was for most of the 
time over the ocean. On asking the teacher how he 
got his data for the measurement, he frankly confessed 



412 EXPOSITION AND ILLUSTRATION IN TEACHING 

that he had no data, but 'thought it would be a very 
effective way of bringing home to the class the enor- 
mous extent of the city." He further wanted to know, 
^^ morals apart/' what objection I had to the illustra- 
tion. The objection is indicated in the incongruity 
brought out above, and also in the mistaken notion 
that in some way or other the imagination of the pupils 
is aided by the picture of this straggling street. After 
all, the figure suggested great extent, but nothing 
more. It carried the pupils far past the Threshold of 
Stun. 

A companion picture to that supplied by this ingen- 
ious teacher is to be found in a text-book of geography 
that seeks to emphasise the progress of London in this 
way: ^' A house rises out of the ground every hour of the 
day; a village of more than three hundred persons is 
added to its population every day." ^ This has ob- 
viously no pictorial value. We certainly do not want 
to figure forth the hourly emergence of a completed 
house, and the very name of a village suggests some- 
thing antipathetic to the city spirit. The mere state- 
ment of a daily increase of three hundred inhabitants 
is sufficiently clear without the obscuring figure. So 
far as the figure is pictorial, it is inaccurate. The popu- 
lation does not increase in that good-naturedly uniform 
way. The figure interferes with the pupil's chance of 
clearly understanding the theory of averages. As a 
matter of fact, in actual experience I have found 
that quite a large percentage of those to whom I have 
presented this illustration have at once accepted the 
arithmetical challenge and multiplied 300 by 365 to get 
the annual increase, and have maintained that the 

^ Meiklejohn : The British Empire, p. 49. 



DANGERS OF ILLUSTRATION 413 

resulting 109,500 was much more stimulating than the 
daily village. 

There may be cases at a very low stage of intelligence 
when a crude illustration of a pictorial kind may enable 
a person to understand in a very inaccurate and in- 
complete wa}^ something that he cannot otherwise 
understand at all. To this class belongs the ingenious 
figure by which one Italian rustic conveyed to another, 
who was puzzled by the telegraph, some conception of 
the possibility of what a man does at one end of a wire 
producing an effect at the other. Starting from the 
well-known fact that if you pinch your dog's tail the 
bark issues from the other end, the expositor invited his 
friend to imagine that his dog grew long enough to reach 
from Milan to Rome, having its tail end in Milan and 
its head end in Rome. It then became clear that, if 
you pinch the tail in Milan, the bark will take place in 
Rome.^ 

In dealing with Exemplification, it is obvious that 
the elements found in the illustration must be cognate 
with those found in the illustrandum. But when we 
are dealing with analogical illustration, it is desirable 
that the material should be different in the two cases. 
This is manifestly true in the aesthetic use, but it also 
holds in didactic work. It is a mistake to use exactly 
the same sort of material in the illustration as is found 
in the illustrandum, unless the very fact of this com- 
munity of material is to be utilised as a part of the illus- 
trative process. If you turn to Chapter V, p. 133, you 

^ The story ends here, but we can imagine the triumph of the dull 
one in pointing out the impossibility of getting through a message 
from Rome to Milan, and the intelligent one's satisfaction in suggesting 
an additional but inverted dog. 



414 EXPOSITION AND ILLUSTRATION IN TEACHING 

will find a case in point. There I wished to illustrate 
the weakness of the negative not as against the positive 
suggestion represented by a noun or a verb. Turning 
my thoughts to the Latin grammar for an example of 
two terms often confused with each other, I found the 
words non and ne had arisen in my mind. They were 
probably suggested by the fact that I was dealing with 
the subject of negatives at the time. In themselves 
they form quite a good illustration, but as soon as I 
reread the passage I saw that there was a certain con- 
fusion likely to arise in the reader's mind. He might 
very naturally think that the Latin negatives as nega- 
tives had something to do with the general subject of 
the paragraph. In any other book I would at once 
have changed the illustration to some other two terms, 
— perhaps scire and cognoscere, — but an example of an 
actual blunder in illustration in the very act of treating 
of illustration was too useful to be thrown aside, so I 
let the blunder stand. Further, no reference was made 
to it in the earlier chapter, in order to give the reader 
an opportunity of testing at a later stage whether he 
could remember any slight confusion having arisen in 
his mind at the time. 

A final danger of the use of certain forms of illustra- 
tion is said to be the tendency it has to make the pupils 
dependent on illustrations for their actual thinking. 
They become incapable, it is said, of doing any thinking 
at all unless suitable illustrations are supplied. They 
never trouble to deal with a generalisation till it is 
followed by illustrations. But it is surely undesirable 
that pupils should be encouraged to accept generalisa- 
tions without examples, and sufficient cautions have 
been already given against allowing the pupil to adopt 



DANGERS OF ILLUSTRATION 415 

a purely passive attitude in respect of illustrations. 
The active reaction of the pupil being secured, he will, 
of necessity, provide certain illustrations of his own. 
Indeed, the supplying of fresh illustrations by the pupil 
is one of the best ways of his securing a mastery over 
the illustrandum. 



CHAPTER XVII 

The Torpedo Shock 

In Plato we find Meno, after being treated on the 
aggravating Socratic method, driven to complain: — 

" Socrates, I used to be told before I knew you that you were 
always doubting yourself and making others doubt ; and now you 
are casting your spells over me, and I am simply getting bewitched 
and enchanted, and am at my wits' end. And if I may venture to 
make a jest upon you, you seem to me both in your appearance and 
in your power over others to be very like the flat torpedo fish, who 
torpifies those who come near him and touch him, as you have now 
torpified me, I think. For my soul and my tongue are really torpid, 
and I do not know how to answer you." ^ 

This is a passage that touches closely all of us who 
concern ourselves with the theory of method in teaching; 
for there is a certain danger that in setting forth more 
or less elaborate theories we may induce a mild form 
of intellectual paralysis in the teachers whom we seek 
to influence. After learning the numberless possibili- 
ties of going wrong, and the small chance of hitting upon 
the absolutely right way to deal with any particular 
case that arises, the student of method may not un- 
naturally become discouraged. There are not lacking 
people who say that to study method is to acquire know- 
ledge that is not only of little use, but is positively 
noxious. Their attitude reminds me of the indignant 
protest of an old college acquaintance of mine, a medical 

^ Meno, 80, A. Jo watt's English. 
416 



THE TORPEDO SHOCK 417 

student, who had just come down in his anatomy: 
'^What's the sense in knowing every miserable nerve 
in the neck ? There's Launceston knows 'em all, and is 
so nervous he's afraid to put in his knife in case he 
severs some of 'em. I don't know 'em, so I've confi- 
dence. I stick in my knife, and there you are." It 
need hardly be said that Launceston was nervous by 
temperament, and not because he was the medallist in 
anatomy. Real, positive knowledge gives power and 
confidence. The man with wide and accurate know- 
ledge is not afraid to give an opinion and act upon it, 
though he has no monopoly of this courage. Neverthe- 
less, there is a certain danger attending the close study 
of method. All the positive principles mastered are of 
direct service in practical work, and your hurriedly 
trained person, with little theory and a great deal of 
practice, is only too willing to lay down the law and 
put it into immediate operation. But the thoughtful 
student who looks all round the subject, and notes this 
defect and the other, even in methods that are on the 
whole excellent, has not the certainty of his less critical 
fellow. The man of criticism is always less confident 
than the man of action. It is important, therefore, that 
critical study should be accompanied by the corrective 
of vigorous practice. The work of the study must be 
brought to fruition in the class room. But this is not 
quite the same thing as to say that the student is to 
carry his theories with him and painfully apply them 
by a conscious effort in front of his class. I have seen 
a man fishing in a pond in Buckinghamshire, with a book 
by his side with the alluring title ^'How to Angle." 
To this he referred when matters became critical — but 
he caught no fish. 

2e 



418 EXPOSITION AND ILLUSTRATION IN TEACHING 

In the stress and strain of the class room the teacher 
must be independent of the book of method. I have no 
doubt that a great deal may be learnt about angling in 
the study, but the riverside is not the place to continue 
the study as study. This is by no means an admission 
that those depressing critics are right who maintain 
that in education theory and practice cannot be harmo- 
nised. ' ' Theory is all very well in the study, but when a 
man gets before a class — " This sort of sentence is 
usually left unfinished, which is a pity. It would be 
pleasant to have a frank statement of the acceptance 
of rule of thumb. 

As a matter of experience there is no difficulty in 
combining theory and practice, but the combination 
cannot be made in the mechanical way that lends 
itself to easy registration in an educational book. The 
matter was put epigrammatically, but with a different 
kind of truth than that the epigrammatist intended in 
the complaint: ''So far as I can gather, students of 
method learn laboriously certain principles that they 
forget the moment they are face to face with a class." 
For the outside observer this is a sufficiently accurate 
description of what takes place; but the inner meaning 
of the change of attitude is apt to be overlooked by 
the casual person. A better description of the same 
phenomenon would be to say that the moment the 
student of method gets before a class he loses conscious- 
ness of the theoretical principles he has been studying. 
It does not follow that those principles have lost their 
influence. It is all a matter of the incidence of con- 
sciousness. Too frequently it is true that theoretical 
considerations do obtrude themselves on the considera- 
tion of the inexperienced teacher when he should be 



THE TORPEDO SHOCK 419 

giving himself up entirely to practice. This means that 
he has not mastered his principles, and therefore is 
unable to forget them in the moment of application. A 
man who has been trained by a proper combination of 
theory and application of theory gradually acquires the 
right to forget all about theory when he is engaged in 
practice. His theory has become a part of himself, 
and affects his activities even when he is not at all 
thinking of theory. The facts of theory have become 
the faculty of practice. 

One of my students told me the other day that she did 
not believe she could begin a sentence with the word 
And, even if she were writing in her sleep, so thoroughly 
had this part of the teaching of the theory of compo- 
sition been assimilated. She remembered that the 
teacher had given her a great many reasons why no 
sentence should ever begin with the word, — reasons 
that many modern authors would dismiss with scant 
ceremony, — but these she could rather guess at than 
remember; the important point is that they had consoli- 
dated themselves into an inveterate rejection of this 
conjunction as the first word in a sentence. 

This little chapter is added mainly to reassure readers 
who may be disturbed by the criticisms that have been 
made of certain illustrations that are not in themselves 
very bad, but are not so good as they might be. The 
reader in his modesty may protest that he will be only 
too glad if in the rough-and-tumble of strenuous teaching 
he can evolve such good illustrations as are held up as 
warnings in these pages, and may feel a little uneasy 
lest in the moment of action some memory of criticism 
may arise and torpify him. From this point of view 
illustrations must be regarded as of two distinct kinds: 



420 EXPOSITION AND ILLUSTRATION IN TEACHING 

those that are prepared for before the lesson, and those 
that are summoned on the spur of the moment to clear 
up more or less unexpected points as they arise. For 
confused or careless illustrations of the first class there is 
never any excuse; but for those of the second class there 
must be great allowance made. Still, the more practice 
the teacher has in preparing good illustrations before the 
lesson, the greater his power of improvising illustrations 
that do not break any of the principles to which he has 
given his assent. In teaching we must let ourselves go : 
the practical interests of the moment must dominate 
everything. But, after all, teaching is not a mechanical 
process. We do not need to leave our minds at the door 
of the class room as the Mohammedan leaves his shoes 
on the mat before entering the mosque. A trained 
rhetorician addressing a public assembly does not think 
of the laws of rhetoric as he makes his appeal. But he 
does apply them. The teacher must be able to think 
on his feet; must be capable of changing an illustration 
in the process of making it; and must all the while de- 
pend upon the paid-up capital of his theorising to keep 
him straight. No doubt he will often make mistakes, 
and will wonder afterwards how, knowing what he did, 
he could have made this blunder and that. But as the 
result of his studies he knows that, in the main, he is 
right. Every blunder he makes gives him something 
to consider after the lesson. But it is to be used in warn- 
ing him against repetitions of this error and its like and 
in strengthening his grip of the positive principles of his 
art, not in discouraging him, and sapping his confidence 
in himself. 



INDEX 



Abstract, place of the, in illustration, 

248; interaction with concrete, 

280-281. 
Abstraction in models, 320, 322. 
Accuracy, excess of, 408. 
Advertising, 22 note, 350, 399. 
^nedd, 105, 138. 

Esthetic illustration, 21-22, 242, 369. 
Alexander, Professor S., 128, 386. 
Algebra, 184. 
Allen, Grant, 192. 
Allen, Professor J. W., 6. 
Alpha Centaur i, 306. 
Alphabetical index, 253, 273. 
Analogy, 73, 90, 91 ; mathematical, 

230 ; spreading of, 232. 
Analysis, the lust of, 64 ; of sentences, 

201. 
Analytic step, 147. 
Anderson, Robert, 310, 379. 
Anticipation, in listening, 15; by 

contraries, 16; in presentation, 

207 note. 
Anticipatory illustration, 31, 32, 33. 
Apperception, 37; masses, 71, 74. 
Application step, 151-152. 
Approaches, kinds of, 226. 
Archimedes, 118. 
Areas, feebleness in estimating, 357 

ff . ; of United States, 364 ; cultiva- 
tion of sense of, 376. 
Aristotle, 230, 234, 240. 
Arithmetic, 176, 281. 
Arithmetical challenge, 250, 309, 332 ; 

(by implication), 402, 412. 
Armstrong, Professor H. E., 34. 
Arnold, Dr., 272. 
Arrest, 71-74, 234. 
Arrows, in diagrams, 386, 388. 
Artists', difficulties in illustration, 

345-347; carelessness, 342. 
Ascham, Roger, 101, 257. 
Association, systematic, 70, 72, 73; 

step, 148; divergent, 292, 402. 



Assumptions underlying theory of 
Formal Steps, 145 ff. 

Attendant circmnstances, 293. 

Attention, 119; rhythm of, 157; in- 
tensity of, 158; incidence of, 400; 
fixed by lines, 385. 

Audiles, 188. 

Author and artist, relations of, in 
illustration, 342 ff. 

Automatic, view of mind, 117-118; 
level, 163. 

Auto-suggestion, 129 ff. 

Awful example, 220, 254. 

Backgrounds: emotional, 92; har- 
monising of, 95; elements of, 97; 
kinds of: fixed, 100; unstable, 
102; mobile, 103; to sermons, 
103; to lectures, 104; temporary, 
107; normal, 122; preferential, 
123; relation to suggestion, 126. 

Bacon, 23, 25. 

Bailey, Philip James, 405 note. 

Bain, Professor A., 116 note. 

Balaclava illustration, 409. 

Baldwin, Professor Mark, 127. 

Ball, Sir Robert, 307-308. 

Barnett, P. A., 389. 

Bates, Charles Austin, 22 note. 

Beginning, 62, 105; degrees of, 179; 
problem of, 178, 179; determines 
order of presentation, 182; condi- 
tions determining, 195; thinking 
a, 278. 

Bell, Sir Charles, 140. 

Bennett and Bristol, 155 note. 

B^ranger, 137. 

Binet and Henri, 384 note. 

Biology, teaching of, 323. 

Bipolar processes and terms, 10. 

Blast-furnace temperature, 301. 

Bosanquet, Professor, 211. 

Botany, teaching of, 322. 

Bourgeoisisme, 294-295. 



421 



422 



INDEX 



Brackenbury, L,, 189. 

Bradley, F. H., 39, 116 note, 230 
note. 

Brain-action, theories of, 88-90. 

British Isles and British Empire, 
position, 327; trade and popula- 
tion, 369 ; 372. 

Browne, Sir Thomas, 150. 

Bruce, Robert the, 96, 97. 

Bullock, J. M., 396, 398. 

Bums, 291. 

Burton, J. Hill, 397. 

Csesar, 154, 321, 322. 

Calder, Mr. John, 387. 

Campe, 173 note, 175 note. 

Caran d'Ache, 381. 

Castellar, Maurice, 140. 

Catalogue elaboration, 287. 

Challenge, arithmetical, 253, 309, 

337; (by implication), 402-403; 

412. 
Chapman, 18. 
Chesterfield, 250. 
Chesterton, G. K., 8 note. 
Chromatists, 336. 
Circle, in diagrams, 374-376; of 

thought, 179. 
Classification, 59-60. 
Clearly imaged ends, 176. 
Collier, Hon. John, 91, 199 note. 
Colour, idea of, 48 ; in diagram, 368 ; 

of shadows, 76, 246; affected by 

canvas, 91. 
Columns in diagrams, 371. 
Combination, false, 209. 
Complex, 64, 98, 102, 198, 287; 

ready-made, 108. 
Complication, 73-74. 
Composition, exercises in, 299. 
Compromise in education, 99. 
Concentration beat, 159. 
Concept, 55 ff. 
Concrete, interpretation of, 245; to 

abstract, 280. 
Confrontation, 79, 80, 81. 
Consciousness, individual and general, 

38; field of, 67-68, 84; distribu- 
tion of, 68; stream of, 68. 
Contenement, 202. 

Continents, area of, illustrated, 359 ff . 
Continuum, 69, 97. 
Contorniates, 218. 



Contradiction and reconciliation, 78. 

Contrariant characters, 132. 

Co-ordinate planes, 333. 

Correlation, excess of, 27; 400. 

Correspondence between inner and 
outer worlds, 54. 

Coteries, 95. 

Coulevain, Madame de, 294-295, 407. 

Countries of Europe, size of, illus- 
trated, 360-361. 

Cramming, 213. 

Cross purposes, 94. 

Cruikshank, 349. 

Cubic content, 377. 

Cubic mile, 311 ff. 

Deductive methods of teaching, 156- 
157. 

Definition, place of, 58; concrete 
form of, 247 ; wider sense of, 294. 

De Garmo, Charles, 147 note. 

Delaware, area, 361. 

Demonstrate, meaning of, 3. 

De Quincey, 6, 11, 242, 243, 244. 

Diagram, imdrawn, 245; distin- 
guished from picture, 348; of the 
seasons, 327-328; place of, in 
teaching, 355; danger of pictorial 
element in, 355 ff . ; two kinds of, 
367; colour in, 368; "of illustra- 
tion," 367, 390. 

Diagrammatic, 352. 

Dialectic, 12 note; Socratic, 276. 

Dickens, Charles, 8 note, 290-291; 
350. 

Diesterweg, 173 note. 

Diffusion beat, 159. 

"Directions," 208. 

Discovery distinguished from apper- 
ception, 236. 

Docendum, 6 note, 11, 26. 

Doyle, Sir A. Conan, 285-286. 

Drayton, 405. 

Drummond, Professor Henry, 230. 

Dunnottar Castle as misleading type, 
113. 

Dynamic view of concept and inner 
world, 57. 

East and west as permanent sugges- 
tion, 138. 
Eastern reliefs, 351. 
Education by deception, 132. 



INDEX 



423 



Elaboration, as school exercise, 276; 
pictorial, 277 ; two forms of, 285- 
286; by catalogue, 287; under 
limitations, 295. 

Eliciting, 153. 

Eliot, George, 398. 

JEmile, 257. 

Emotional background, the, 92. 

Ending, 184 ff. ; as termination, 
184. 

Eniuneration, 289-291. 

Estimate of cubic content, 377-378. 

Ethics, 268. 

Euclid, 333, 390. 

Euler's Theorem, 33, 154. 

Exaggerations necessary, 407. 

Example and precept, 268. 

Examples, too attractive, 398 ; stere- 
otyped, 393. 

Exceptions, 222-223. 

Excluded middle, 40, 86. 

Explanation, 5, 7, 8, 76 ; subordinate, 
203. 

Expositandum, 11, 161. 

Exposition, by pupil and by teacher, 
4; data of, 5; bipolar, 9; essen- 
tially constructive, 60, 61, 63; 
destructive stage of, 62; unit of, 
64; relativity of, 160; starting- 
point of, 168; possibility of too 
good, 210-211; distinguished from 
illustration, 18, 257; to class as 
opposed to individuals, 225. 

Expound, meaning of, 2. 

Fable, need for details in, 270 ; truth 
in, 271. 

Fact and faculty, 63, 162, 419. 

Facts, explanation and interpreta- 
tion of, 5-6; organised, 161; of 
co-ordinate rank, 201. 

Faculties, 44 ff. 

Fairytales, 272. 

Fait accompli, 342. 

Fatigue diagram, 384. 

Faust, 257. 

Field of consciousness, 67, 68 ; 84. 

Finger-post criticism, 25, 26. 

Fixed backgrounds, 100. 

Fluid minds, 101. 

Focal ideas, 67, 129. 

Foreign suggestion, 129. 

Formal Steps, 145 ff.; errors in 



application of, 152; in notes of 

lessons, 154. 
Frankland, Dr. Edward, 170 note, 

331,332. 
French, order of adjectives in, 190; 

auxiliary verbs, 393. 
Frith, W. P., 347. 
Froehener, M., 218. 
Fuller, Thomas, 22, 23. 
Fusion, 73, 74, 234. 

Galton, Francis, 279. 
Gaping Point, 163 ff., 277. 
Garnett, Dr. William, 120 note. 
Geikie, Sir Archibald, 188. 
Generalisation, 36, 155, 199, 262, 

354; step, 148-149. 
Geography, 183; commercial, 182; 

text-book, 318. 
Geometry, the new, 184; descriptive, 

333. 
German, vocabulary, 28 ; possessives, 

193; rule as to gender, 225. 
Globes, the, 327. 
Glyptic formula, 331-332. 
Grammar, teaching of, 188. 
Granger, Rev. James, 396. 
Grangerising, 396. 
Greek education, 211. 
Growing Point, 162. 
Guy Fawkes, 338. 
Guyau, J. M., 127. 

Hamilton, Anthony, 180. 

Hamilton, Clayton, 203. 

Hamilton, Sir William, 40, 70. 

Hardewittes, 101. 

Harris, Dr. W. T., 142 note. 

Hartmann, Dr. Berthold, 98 note. 

Hay, Ian, 222. 

Hayricks, painted, 337. 

Hayward, Dr. F. H., 318. 

Helvetius, 406. 

Herbart, 145, 146, 147. 

Herschel, Sir John, 329, 330, 331, 408. 

Heuristic method, 32, 172, 173. 

Hill, Burton, 397. 

History, 183; imder different pow- 
ers, 160; text-book in, 293, 294; 
pictures in teaching of, 338; 
"true" pictures in, 339. 

Hobbes, 275 ; credit system, 276. 

Hodgson, Shadworth H., 116. 



424 



INDEX 



Hofmann, 331. 

Homer, 251, 288. 

Homonyms, 123. 

Howatt, Rev. J. R., 289. 

Hugo, Victor, 293. 

Hume, 48. 

Huxley, Professor T. H., 48, 77 

notes. 
Hypostasis, 44, 45, 46. 

Iconographs, 139-140. 

Ideas, 40; distinguished from facul- 
ties, 45; as material of thought, 
46; as forces, 46-47; interaction 
of, 47; focal and marginal, 67; 
realisation of, 72, 275; complica- 
tion and fusion of, 73; as perma- 
nent potentialities, 84 ; in subcon- 
scious state, 87-89 ; complexes of, 
98; organisation of, 99; breaking 
up of complexes of, 169-170; re- 
call of, 104; ready-made com- 
plexes of, 99; mediate and im- 
mediate recall of, 119; conditions 
of recall of, 122; development in 
consciousness, 283. 

Idie fixe, 99, 100. 

Identity, principle of, 39; sense of, 
69. 

Illustrandum, 19, 28, 30, 31, 232, 235, 
241, 312, 320, 321, 327; cognate 
with illustration, 413; mastery 
over, 415. 

Illustrate, meaning of, 18, 19. 

Illustration, distinguished from ex- 
position, 18, 257; in a circle, 27; 
as a sedative, 22; anticipatory, 
31, 32; twofold classification of, 
229; verbal and material, 317; 
teacher's use of the incidental of, 
207; classification of, 319; hand- 
to-mouth method of, 392; over-, 
395; misplaced pictorial, 411; 
pupils dependent on, 414; dia- 
grams of, 367, 387. 

Illustrations, interstitial, 23; di- 
dactic use of, 242; misleading, 
242; stock of, 393; carried over 
bodily, 408; prepared and extem- 
pore, 419-420. 

Illustrative enumeration, 290-291. 

Imagery, visual, 385. 

Images, 55; generalised, 56. 



Immediate recall, 119. 

Impressionability, threshold of, 300; 
zone of, 303. 

Impressionists, 336. 

Incidence of external influence in 
suggestion, 129. 

Incidental references, 205, 207. 

Induction, 32, 33. 

Inductive methods of teaching, 156, 
157. 

Inference point, 161, 162, 277. 

Information, 153, 292, 319. 

Inhibition, 71. 

Instruction, 153. 

Inter-aims, 173. 

Intercourse, 51. 

Interest, rhythm of, 186; in relation 
to recapitulation, 226-227; de- 
railing of, 400; killing of, 404, 407. 

Interstitial, vision, 13; illustrations, 
23. 

Introductions, 179. 

Isocrates, 244. 

Ivanhoe, 339, 344 note. 

Jacotot, 2, 3; Jacototian, 379. 
James, Professor William, 15, 68, 

103, 232, 233. 
Janet, Professor Pierre, 127. 
Joe Millers, religious, 273. 
Johnson, Dr., 132, 407. 
Johnston, F. W., 22 note. 

Keatinge, M. W., 129, 132. 

Key, 31 note. 

Knowledge, reproduction of, 50 ; not 

yet due, 153, 394. 
Knox, John, 49. 

La Fontaine, 257, 262, 263, 270. 

Lamb, Charles, 237-238. 

Landois, 77 note. 

Language, teacher's use of, 387. 

Latin, genders, 27-28; oratio ohli- 
qua in, 31 ; order of teaching, 61 ; 
negatives, 133, 414; method of 
teaching, 157; from abstract to 
concrete in, 200; grammars and 
exceptions, 223; Latin Compara- 
tive, 229; cum with subjunctive, 
392; examples in grammar, 398. 

Law stage, 55. 

Laws of Thought, 40, 75. 



INDEX 



425 



Lawson, William, 310. 
Lectures, lantern, 23, 26. 
Lecturing, 12. 
Lesson-lengths, 173. 
Leutz, Ferdinand, 174 note. 
Liebig, Baron, 20. 
Listening, analysis of, 12 ff. 
Liverpool, Lord, 269 note. 
Locke, John, 41 note, 85. 
Lodge, Sir Oliver, 207. 
Logic, 86, 269. 
Logical presentation, 187 ff. 
Lucas, E. v., 14, note. 

Macaulay, Lord, 284. 

Macdougall, W., 10 note, 126, 127, 
388. 

Macdowall, K. A., 218. 

Macleod, Norman Islay, 269. 

Macturk, John, 363. 

Magna Charta, 201. 

Marshall, Professor, 385. 

"Match drawing," 382. 

Material, 319. 

Materialism, 88. 

Mathematics, 9, 61, 183. 

Mauclair, Camille, 337. 

Maxwell, J. Clerk, 368. 

Mediate recall, 119. 

Meiklejohn, Professor, 412. 

Meno, 368 note, 416. 

Mental activity, 116, 131. 

Mental content, 38, 41, 42, 61, 138, 
156; analysis of, 167; overlap of, 
168; organisation of, 192; com- 
mon segment of, 225, 277; limits 
of organisation of, 163, 411. 

Mental focus, 158; sliding scale of, 
160. 

Mental harmony, law of, 75. 

Mental imagery, 280-281. 

Mental parallax, 113. 

Mental pictures, 108, 111, 277; ex- 
ternal standard of, 112. 

Metaphor, 130; as analogy, 231; 
conditions of, illustrative use of, 
232; dangers of, 234; relation to 
illustrandum, 235 ff. ; cumulative 
effect of, 238; one-sided, 240. 

Method, deductive and inductive, 
156-157; Socratic, 80 ff., 96, 172, 
174-175; heuristic, 32, 172, 173; 
dangers of study of, 416 ff. 



Metric system, 211. 

Metrical diagrams, 367. 

Mill, J. S., 19, 200. 

Million, meaning of, 298, 

Milton, 240, 403, 405. 

Minds, kinds of, in respect of back- 
grounds, 98; rigid, 98; fluid, 101; 
plastic, 103; the associative, 102. 

Minimum suggestible, 141. 

Mistake-traps, 221. 

Mitchell, Professor W., 131. 

Mitchill and Carpenter, 4 note, 306. 

Model, the, 317; relation to real 
object, 319; as type, 323; three 
dimensions of, 324, 326, 330; im- 
reality of, 325; relation to senti- 
ments, 325; contrast with dia- 
gram, 328 ; made by pupils, 334. 

Monet, Claude, 336. 

Moral, place of the, 267 ; child's view 
of the, 270. 

Mot 'propre, 189. 

Multiplication through addition, 29. 

Murray, Dr. J. A. H., 249. 

Myers, Dr. C. S., 349. 

Narrative, 203. 

Nathan the prophet, 214, 215. 

Nebuchadnezzar's furnace, 300. 

Newton, Dr. Richard, 254, 256. 

Niagara, 301, 304, 311. 

Nicholson, Professor H. A., 59. 

Non-contradiction, law of, 40. 

Norris, Frank, 339. 

North, Lord, 135. 

North Carolina, area of, 359. 

Novelist's anticipatory references, 

205. 
Nunn, Dr. T. Percy, 206, 219, 334, 335. 

Object lessons, 64. 

Objective standard in illustration, 
344. 

Objects, 317. 

Observation frequency polygons, 384. 

Ohm, 120. 

Onions, Oliver, 136. 

Order, of substantive and objective, 
190-191; of figure and illustra- 
tion, 241. 

Order of presentation, determined by 
beginning, 195; by practical con- 
siderations, 208. 



426 



INDEX 



Originality in lectures, 14. 
Ornithorh5nichus, 59-60. 
Orrery, 328. 

Orthographic story, 180. 
Osier, Dr. W., 239, 240. 

Paradise Lost, 405 note. 

Paragraph, the first, 178; illustrative 
of bad order, 205. 

Parallelism between physical and 
mental, 89. 

Passive poets, 341. 

Paterculus, 242, 244. 

Paulhan, Fr., 70, 71, 117. 

Pearson, Professor Karl, 384. 

Percentages and suggestion, 137. 

Perspective, 8, 345, 350. 

Petit, M. Edouard, 349. 

Pictorial, the, 306, 355; diagram, 
complication of, 356-357. 

Picture, limits imposed by, 340 ; two 
conditions of use of, as historical 
illustration, 339; as illustrating 
poetry, 341; infidelity of illus- 
trative, 341 ff. ; in text-books, 
347; distinguished from diagram, 
348; informative aspect of, 349- 
350; in advertisement, 350; clas- 
sification of, in order of abstract- 
ness, 352; place of, in teaching, 
355. 

Pictures, mental, 277-280. 

Plastic mind, 103. 

Plato, 250, 251, 253, 254, 416. 

Poe, Edgar Allan, 130, 241 note. 

Point of view, 1, 113. 

Polyolhion, 405 note. 

Portraits, 337. 

Preaching, 11. 

Preferred, apperception mass (or 
backgroimd), 120, 123, 125; sense, 
the, 108-109; ideas, 68. 

Premature conception, 214, 242. 

Preparation Step, 147, 167. 

Presentation, 145; order of, 146; 
falsity and incompleteness of, 219 ; 
logical, 187 ff., 199; preliminary 
conditions of, 195; bad order of, 
205. 

Presentative activity, 66-67, 74, 120. 

Presented content, 65, 93. 

Primary colours, 169; psychological, 
170. 



Primer on Teaching, 387. 
Problems, 182, 217. 
Prompting, 135. 
Pseudo-auto-suggestion, 129. 
"Psychic fringes," 284. 
Psychology, 86, 268; of listening, 12. 
Pupil, as technical term, 11. 
Purpose unit, 173. 

Qualitative and quantitative reason- 
ing, 385. 
Quotation marks, 394. 

Ramsay, Sir W., 318. 

Raven, Rev. J. H., 31. 

Reading, 14. 

Realising, ideas, 72, 275; figures, 
291 ; sizes and nimibers, 297. 

Reality in models, 325. 

Recall, 104; conditions of, 122; 
mediate and immediate, 119. 

Reconstruction, 214. 

Redintegration, 134. 

"References forward," 207. 

Relative sizes of countries and conti- 
nents, 359-304. 

Relativity, in exposition, 160; in 
manipulating vast nimibers, 309- 
311. 

Rennet, Dr. David, 213. 

Republic, the, 250. 

Rhythm, of attention, 157; in teach- 
ing, 179; of interest, 186; of ab- 
stract and concrete, 199. 

Richter, Jean Paul, 235 note; 268 
note. 

Richter, Karl, 173 note. 

Rickerton Medal, 176. 

Riddle, 240. 

Right and left, confusion of, 114. 

Rigid minds, 98. 

Romanes, G. J., 349. 

Rothschild, Nathan, 267, 269, 270 
note. 

Rousseau, 257 ff., 326. 

Rule, and exception, 222 ff. ; and 
example, 228. 

"Rules," 222, 282. 

Ruskin, 8, 298. 

Saving pupils trouble, 210. 
Scansion, 216. 
Science teaching, 217. 



INDEX 



427 



Scott, Sir W., 237, 339, 350. 

Self-activity, 130. 

Self-referent tendency, 265. 

Sentences, loose and periodic, 248. 

Shadows, colour of, 246. 

Shakespeare, 15, 25, 78. 

Shelley, 15. 

Sidis, Dr., 132. 

Silhouettes, Chinese, 140. 

Silvestre, M. J. B., 139. 

"Simple" and "easy to understand," 
198. 

Simplon Tunnel, 182. 

Sirius, 309. 

Socrates, 80, 250-251, 416. 

Soft pedagogy, 212. 

Spencer, Herbert, 76, 169, 189-190, 
196, 197, 198, 205, 214, 246, 279. 

Sprachgefuhl, 44. 

Standard, area, 315, 360; for differ- 
ent powers, 160; map of West of 
Old World, 380. 

Starting-point of exposition, 167. 

Static view of concept and inner 
world, 57. 

Stephens, Winifred, 294. 

Stevenson, R. L., 271. 

Stirling, Hutchison, 277, 278, 280. 

Story, three uses of, 251 ; the in- 
vented, 271 ; sources of, 273. 

Stout, Professor G. F., 42, 116, 128, 
284. 

Straight lines in diagram, 353, 371, 
378. 

Stun, Threshold of, 301, 302, 303, 
304, 306, 307, 313, 412; raising of, 
305. 

Style, test of, 7; tmderlying, 16; 
philosophy of, 189; allusive, 403, 
405. 

Subconscious, the, 85; physical 
correlate of, 87-88. 

Subjunctive, 222, 392. 

Substantive, elements of thought, 43, 
73, 125; meaning, 123. 

Sufficient reason, law of, 40. 

Suggestion, external, 122; Wundt's 
and Thomas's definitions, 128 
Baldwin's and Janet's definitions, 
127; auto-, 128; foreign, 129 
pseudo-auto-, 129; unilateral, 133 
relation to apperception, 134 
permanent, 135, 159, 371 ; moral 



justification of, 143; as an end, 
143-144; most obvious kind, 350. 

Superlative references, 404. 

Superstition, one function of, 75. 

Synthetic step, 147. 

System, stage of, 55; step, 147, 149. 

Tactiles, 109. 

Teaching, six principles of, 196-197; 

criticism of six principles of, 197 

ff. ; by text-books, 318; deductive 

and inductive methods of, 156- 

157; to class, 226. 
"Telling," 153. 
Temptation, 144, 256-257. 
Tennyson, 235, 288, 402-403. 
Theory and practice, 419. 
Therefore, use of, 165-166. 
"Thing stage," 44, 55. 
Thing-in-itself, 53. 
Thinking, atomistic, 15; small change 

type of, 277; pictorial, 278-279. 
Thomas, Professor P. E., 127. 
"Thorough," 159. 
Thought, laws of, 39, 75; swiftness 

of, 281. 
Threshold, 85 ; of Consciousness, 86 ; 

of Impressionability, 300-303; of 

Stun, 301-307, 412. 
Time-imit, 174. 
Transitive, elements of thoughts, 43 ; 

meaning, 125. 
Trapp, E. Ch., 171. 
Turbid media, 91. 
Type, the, as illustration, 247. 

Unconscious humour, 411. 

Unit, time and purpose, 174; size 

of, 204; general treatment of, 204; 

highest available, 315; standard, 

315-316, 360. 
United States, area of, 364. 
Units, 66. 
Unstable backgrounds, 102. 

Vacuum, the, in exposition, 216 ff. 

Velasquez, 337. 

Veronese, 339. 

Virgil, 105. 

Vision, interstitial, 13; field of, 14. 

Visuals, 108. 

Vorstellung, 278, 283. 



428 



INDEX 



Wallas, Graham, 384-385. 

Walpole, Horace, 284. 

Ward, Dr. Jaraes, 386. 

Weariness from over-correlation, 27, 

400. 
Webster, dictionary, 17, 249. 
Wells, H. G., 301, 304. 
Whately, 130 note. 
Whitman, Walt, 287, 288, 346. 
Whittier, 171. 
Wight, Isle of, 314. 
Wilmann, Otto, 196. 
Witmer, Lightner, 171, 359. 



Witt, Robert Clermont, 348. 
Wolf, Lucien, 270. 
Wordsworth, 99, 271. 
Worlds, inner and outer, 51 ff. 
Wright, Professor Mark, 12. 
Wmidt, 128, 129. 

Zielangahe, 171 ff., 175, 184, 268. 
Ziller, Tusikon, 171, 174 note, 197 

note. 
Zone of impressionability, 303. 
Zwischenziele, 173, 176, 185. 



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BAGLEY, William Chandler. Classroom Management : Its Principles 
and Technique. By William Chandler Bagley, Superintendent of the 
Training Department, State Normal School, Oswego, N.Y. 

Cloth. i2mo. XVU+JJ2 pages. $i.2§ net. 

The Educative Process. Cloth. Z2mo. xix-\- 358 pages. $1.25 net. 

BROWN, John Franklin. The American High School. By John Frank- 
lin Brown, Ph.D., formerly Professor in Education and Inspector of High 
Schools for the State University of Iowa. 

Cloth, xii + cfg8 pages. i2mo. $i.2§ net. 

BUTLER, Nicholas Murray. The Meaning of Education, and Other 
Essays and Addresses. By Nicholas Murray Butler, President of Colum- 
bia University. Cloth. i2mo. xii -\r 230 pages. $1.00 net. 

CHUBB, Percival. The Teaching of English. By Percival Chubb, Princi- 
pal of High School Department, Ethical Culture School, New York. 

Cloth. Z2mo. xvii -\- 411 pages. $1.00 net. 

COLLAR, George, and CROOK, Charles W. School Management and 
Methods of Instruction. By George Collar and Charles W. Crook, 
London. Cloth. i2mo. viii-\-jj6 pages. $1.00 net. 

CRONSON, Bernard. Methods in Elementary School Studies. By 
Bernard Cronson, A.B., Ph.D., Principal of Public School No. 3, Borough 
of Manhattan, City of New York. Cloth. i2mo. ibj pages. $1.25 net. 

Pupil Self-Government. Cloth. i2mo. ix + loj pages. $.go net. 

CUBBERLEY. Syllabus of Lectures on the History of Education. With 
Selected Bibliographies and Suggested Readings. By Ellwood P. Cub- 
berley. Second Edition, revised and enlarged. In two parts. 

Part I,v-\- 1 2g pages, $i.§0 net ; Part II, xv -\-j6r pages, $1.^0 net. 

Complete in one volume, $2.60 net. 

DE GARMO, Charles, Interest and Education. By Charles De Garmo, 
Professor of the Science and Art of Education in Cornell University. 

Cloth. i2mo. xvii-\r 2J0 pages. $1.00 net. 
The Principles of Secondary Education. 

Vol. I, Studies. Cloth. i2mo. xii ■\- 2gg pages. $i.2§ net. 

Vol. II, Processes 0/ Instruction, xii + 200 pages. $1.00 net. 

Vol. Ill, Processes of Instruction. In press. 

DEXTER, Edwin Grant. A History of Education in the United States. 

By Edwin Grant Dexter, Professor of Education in the University of Illinois. 

Cloth. xxi-\- 665 pages. 8vo. $2.00 net. 

DUTTON, Samuel T. Social Phases of Education in the School and the 
Home. By Samuel T. Dutton, Superintendent of the Horace Mann 
Schools, New York. Cloth. i2mo. ix -\- 2^g pages. $1.2^ net. 

DUTTON & SNEDDEN. The Administration of Public Education in the 

United States. Bv Samuel Train Dutton, A.M., and David Snedden, 

Ph.D. With an Introduction by Nicholas Murray Butler, Ph.D., LL.D. 

Cloth, via -\- sgs pages. Bibliography. Index, i2mo. $i.j§ 7iet. 



A LIST OF BOOKS FOR TEACHERS — Cbnfmaec/ 



FITCH, Sir Joshua. Educational Aims and Methods. Lectures and Ad- 
dresses by Sir Joshua Fitch, late Her Majesty's Inspector of Training 
Colleges. Cloth. xii-\- 448 pages. i2mo. $i.2§ net. 

Lectures on Teaching. Cloth. xiii-\-jgj pages. i6mo. $1.00 net. 

GILMAN, Mary L. Seat "Work and Industrial Occupations. A Practical 
Course for Primary Grades. By Mary L. Gilman, Principal of the Clay 
School, Minneapolis, Minn., and Elizabeth L. Williams, Principal of the 
Holmes School, Minneapolis, Minn. 

Fully illustrated. Cloth. 141 pages. Square i2mo. $.50 net. 

GANONG, William F. The Teaching Botanist. By William F. Ganong, 
Ph.D., Smith College. Cloth, rsmo. xi-[- s'^o pages. $1.10 net. 

GRAVES, Frank P. A History of Education before the Middle Ages. By 
Frank Pierrepont Graves, Ohio State University. 

Cloth. J20 pages. Bibliography. $t.io net. 

HALLECK, Reuben Post. The Education of the Central Nervous System. 

A Study of Foundations, especially of Sensory and Motor Training. By 
Reuben Post Halleck, M.A. (Yale). 

Cloth. i2mo. xii + 258 pages. $1.00 net. 

HANUS, PAUL H. A Modem School. By Paul H. Hanus, Professor of the 
History and Art of Teaching in Harvard University. 

Cloth. i2mo. X -\- ^06 pages. $1.2^ net. 

Educational Aims and Educational Values. By Paul H. Hanus. 

Cloth. i2mo. vii-\- 221 pages. $1.00 net. 

HERBART, John Frederick. Outlines of Educational Doctrine. By John 
Frederick Herbart. Translated by Alex. F. Lange, Associate Professor of 
English and Scandinavian Philology and Dean of the Faculty of the College 
of Letters, University of California. Annotated by Charles De Garmo, 
Professor of the Science and Art of Education, Cornell University. 

Cloth. Large i2nio. xi + 334 pages. $1.25 net. 

HERRICK, Cheesman A. The Meaning and Practice of Commercial Edu- 
cation. By Cheesman A. Herrick, Ph.D., Director of School of Com- 
merce, Philadelphia Central High School. 

Cloth. XV -\- 3^8 pages . j2mo. $1.25 net. 

HORNE, Herman Harrell. The Philosophy of Education. By Herman 
Harrell Home, Assistant Professor of Philosophy and Pedagogy in Dart- 
mouth College. Cloth. 8vo. xvli-\- 2gs pages. $1.^0 net. 

The Psychological Principles of Education. By Herman Harrell Home. 

Cloth. i2mo. xiii + 43S pages. $1.75 net. 

HUEY, Edmund B. The Psychology and Pedagogy of Reading. By Pro- 
fessor Edmund B. Huey, of the Western University of Pennsylvania. 

Cloth. i2mo. xvl + 46g pages. $1.40 net. 

JONES, Olive M., LEARY, Eleanor G., and QUISK, Agnes E. Teach- 
ing Children to Study. The Group System applied. 

Illustrated. Cloth, viii + ig3 pages. i2mo. $.80 net. 

KILPATRICK, Van Evrie. Departmental Teaching in Elementary 
Schools. By Van Evrie Kilpatrick. 

Cloth. i2mo. xiii -h 130 pages. i6mo. $.60 net. 



A LIST OF BOOKS FOR TEACHERS — ConfmaedT 



KIRKPATRICK, EDWIN A. Fundamentals of Child Study. By Professoi 

Edwin A. Kirkpatrick, Principal of State Normal School, Fitchburg, Mass. 

Cloth. i2mo. xxi-\- 284 pages. $1.25 net. 

MAJOR, David R. First Steps in Mental Growth. A Series of Studies in 
the Psychology of Infancy. By David R. Major, Professor of Education 
in the Ohio State University. 

Cloth. xiv-\-j6o pages. i2mo. $1.25 net. 

THE McMURRY SERIES Each, doth. 12mo. 

General Method. 

The Elements of General Method. By Charles A. McMurry, 

323 pages. $.go net, 

The Method of the Recitation. By Charles A. McMurry and Frank M. 

McMurry, Professor of the Theory and Practice of Teaching, Teachers 
College, Columbia University. xi-\-32g pages. $.gonet. 

Special Method. By Charles A. McMurry. 

Special Method in Primary Reading and Oral Work with Stories. 

vii + 103 pages. $ .60 net. 

Special Method in the Reading of English Classics. 

vi + 254 pages. $.7s net. 

Special Method in Language in the Eight Grades. 

viii + ig2 pages. $.yo net. 

Course of Study in the Eight Grades. 

Vol.1. Grades I to IV. vii -\- 236 pages. %.j§ net. 

Vol.11. Grades V to VIII. v-\- 226 pages. $.^3 net. 

Special Method in History. vii + 297 pages. ^.75 net. 

Special Method in Arithmetic. vii + 225 pages. $.jo net. 

Special Method in Geography. xi-\- 217 pages. $.70 net. 

Special Method in Elementary Science. ix + 273 pages. $.73 net. 

Nature Study Lessons for Primary Grades. By Mrs. Lida B. McMurry, 

with an Introduction by Charles A. McMurry. xi + igi pages. $.60 net. 



MONROE, Paul. A Brief Course in the History of Education. By Paul 
Monroe, Ph.D., Professor in the History of Education, Teachers College, 
Columbia University. Cloth. 8vo. xviii-\- 4og pages. $1.23 net. 

A Text-book in the History of Education. 

Cloth, xxiii + 277 pages. i2m.o. $i.go net. 

A Source Book of the History of Education. For the Greek and Roman 

Period. Cloth. xiii-{- 313 pages. 8vo, $2.23 net. 

O'SHEA, M. V. Dynamic Factors in Education. By M. V. O'Shea, Pro- 
fessor of the Science and Art of Education, University of Wisconsin. 

Cloth. i2mo. xiii -\- 320 pages . ^/. 25- net. 

Linguistic Development and Education. 

Cloth. i2mo. xvii-\- 347 pages, $1.23 net. 



A LIST OF BOOKS FOR TEACHERS— Cbn^mtrecf 



PARK, Joseph C. Educational Woodworking for Home and School. By 

Joseph C. Park, State Normal and Training School, Oswego, N.Y, 

Cloth. i2tno. xiii-{- jro pages, illus. $i.oonet. 

PERRY, Arthur C. The Management of a City School. By Arthur C. 
Perry, Jr., Ph.D., Principal of Public School No. 85, Brooklyn, N.Y. 

Cloth. i2nio. viii -\- 350 pages. $1.25 net. 

ROWE, Stuart H. The Physical Nature of the Child. By Dr. Stuart H. 
Rowe, Professor of Psychology and the History of Education, Training 
School for Teachers, Brooklyn, N . Y. 

Cloth. i2mo. vi-\- 211 pages. $.gonet. 

ROYCE, JosiAH. Outlines of Psychology. An Elementary Treatise with 
some Practical Applications. By Josiah Royce, Professor of the History 
of Philosophy in Harvard University. 

Cloth. i2mo. xxvu-\-jg2 pages. $1.00 net. 

SHAW, Edward R. School Hygiene. By the late Edward R. Shaw. 

Cloth. vii-\- 255 pages. i2mo. $1.00 net. 

SHURTER, Edwin DuBois. The Rhetoric of Oratory. By the Associate 
Professor of Public Speaking in the University of Texas. 

Cloth. J2J pages. i2mo. $1.10 net. 

SMITH, David E. The Teaching of Elementary Mathematics. By David 
E. Smith, Professor of Mathematics, Teachers College, Columbia Uni- 
versity. Cloth. xv-\-ji2 pages. i2mo. $1.00 net. 

SNEDDEN AND ALLEN. School Reports and School Efficiency. By David 
S. Snedden, Ph.D., and William H. Allen, Ph.D. For the New York 
Committee on Physical Welfare of School Children. 

Cloth. i2mo. xi -\- i8j pages. $1.^0 net. 

VANDEWALKER, Nina C. The Kindergarten in American Education. 
By Nina C. Vandewalker, Director of Kindergarten Training Department, 
Milwaukee State Normal School. 

Cloth. xiii-\- 2^4 pages. Portr., index, i2mo. $1.25 net. 

WARNER, Francis. The Study of Children and Their School Training. 
By Francis Warner. Cloth, xix + 264 pages. j2mo. $1.00 net. 

WINTERBURN AND BARR. Methods in Teaching. Being the Stockton 
Methods in Elementary Schools. By Mrs. Rosa V. Winterburn, of Los 
Angeles, and James A. Barr, Superintendent of Schools at Stockton, Cal. 

Cloth. xii-\-j^^ pages. i2mo. $1.23 net.- 



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